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23 November 2024 18:20
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Welcome to the gyroscope forum. If you have a question about gyroscopes in general,
want to know how they work, or what they can be used for then you can leave your question here for others to answer.
You may also be able to help others by answering some of the questions on the site.
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Question |
| Asked by: |
Luis AE Gonzalez |
| Subject: |
How precession works in a toy gyro - Why precession has no centripetal / centrifugal force |
| Question: |
This is not a question but a clarification of some gyro concepts (no answers are requested).
An object in circular motion is constantly PULLED-IN toward the center of rotation. The pulling-in toward the center (centripetal force) is what keeps the object from continuing to move in a straight line.
The flywheel of a toy gyro in precession REPOSITIONS itself, to align its spin with the direction of the circular force of the torque applied. In the process of Repositioning, the flywheel makes the necessary adjustments dictated by the rigid support (axle) that attaches the flywheel to the pivot point (the point that we perceive as the center of precession).
In other words, the flywheel in precession changes position so that it will eventually lineup and spin in the same direction as the circular force of the torque (you can verify this).
There is no need for pulling-in toward the center because precession is not trying to convert a straight line motion into a curve.
Precession is in fact extending its change in directional attitude to the configuration in which it is attached to a pivot point. (Does this need more explanation?)
Note – if the flywheel were to allow itself to be carried by the applied torque, then it would NEVER end up lining up its spin with the spin that the applied torque is trying to create.
Can you see this?
The interesting thing is that the gyro in a tower can never lineup with the torque of gravity because gravity provides a LINEAR force. Why?!
Though the gyro perceives gravity as a circular torque (because the tower holds up the opposite end of the axle while the gyro mass is not supported), still gravity is really only pulling the gyro downwards (and not fully around).
As the gyro under gravity moves, to try to catch up with the torque axis, the axis of torque continues to move ahead, and the gyro can never catch up with it (because gravity is a linear force). (A 3-D model will help.)
That is why a gyro on a tower, under gravity continues to do turn after turn in precession.
On the other hand an applied torque causes precession that stops at a point of balance. The point of balance is where the spin axis of the gyro flywheel is in line with the spin direction of the torque applied. Is this clear?
Can you see that an applied torque is a circular force while gravity is a linear force downward?
The single most important thing we can know about gyros is that precession occurs purely at the flywheel of the gyro, and no where else.
The translation of a toy gyro on a pedestal (or a gyro climbing when a torque is applied), are peripheral interactions that we have come to identify as precession itself. The fact is that at the core of these precession phenomena, the root cause is the flywheel seeking to change its spin axis (and/or its spin plane) to match the circular direction of motion of the perceived torque.
To become better acquainted with these concepts, focus ONLY on the response of the flywheel, and understand it, then all the other observations start falling into place and we are able to explain, why precession does not have a force (e.g. why the tower doesn’t slide during precession).
Here is an intuitive view of precession in its simplest form (just the flywheel).
Consider that a spinning wheel is actually an object in motion (though somewhat more complex than straight-line motion).
Consider that a torque is basically an angular force (around a curve instead of in a straight line).
Consider that when an object traveling in straight-line-motion is affected by a force, the direction of the object is affected toward the direction in which the force is applied.
Similarly, when torque (a circular force) is applied to a spinning wheel (a moving object), the applied torque affects the position of the wheel toward a direction where the wheel will spin in the same direction in which the torque (circular force) is applied, in other words both spin axis will be the same or parallel and the respective spins will be in the same direction.
Thank you, Luis
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| Date: |
16 May 2006
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Answers (Ordered by Date)
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| Answer: |
Luis Gonzalez - 21/05/2006 20:15:40
| | | [This is the second in a series of statements about a theory of mechanical propulsion. Answers are NOT requested to the rhetorical questions contained. I ask that you please put your remarks and questions in a separate thread.]
We know that gyros respond with a ‘fresh direction’ of precession under the following conditions:
1) When acted upon by an incongruously directed torque (that seeks to change the spin axis)
2) When obstacles interfere, forcing precession to find a new direction of motion
Both interactions are treated as forces, the first one as a force to change the axis of alignment, and the second one as a force to change the direction in the forward progress of existing precession.
Converting the kinetic energy of precession into a linear force:
Precession responds at 90-degrees to obstacles because obstacles present a stopping FORCE. This 90-degree change in direction (from the vector of incidence to the resulting vector of precession) involves a very interesting exchange of energy and forces.
Compare the Force of impact delivered by the velocity of deadweight with the Force delivered by the velocity of an object moving in precession. (In his Christmas Lecture # 15 at http://www.gyroscopes.org/1974lecture.asp Laithewaite failed to conclusively demonstrate that a moving deadweight carries more kinetic energy than the equivalent motion of a gyro in precession. I still believe it is possible that an object in precession delivers a weaker punch, because it appears to change direction with greater ease than deadweight in motion.)
In a head-on impact, the deadweight would appear to deliver a stronger force because it bounces back from the impact at 180 degrees from the original direction of velocity. On the other hand, an object in precession responds at 90 degrees, and one expects the 90 degree response to create a lower energy exchange in such a collision.
The important thing is that both (the moving deadweight and precession) deliver a significant wallop. Review of Christmas Lecture # 15 demonstrates that both collisions shook the platform and caused a significant thud; energy was exchanged in both cases. When precession encounters an obstacle, an exchange of energy occurs with a magnitude proportional to the kinetic energy in the velocity of precession (though an adjustment may be necessary since the exchange of energy results in a 90 degree change, instead of the classical 180 degrees).
Here is another perspective of the energy exchange mentioned above:
Most of us are aware that the torque applied (to cause precession) creates an equal and opposite reaction (manifested by a counter-torque, due to the interaction of the torque with the gyro’s inertia / mass).
In a similar manner, changing the direction of precession (by using an obstacle) should produce a degree of counterforce upon the component that is supplying the obstacle to affect the direction of precession (the magnitude of this counterforce may be somewhat diminished by the relatively limited velocity of the resulting precession).
The transition of precession from one vector to another (through 90 degrees) is often so smooth that we frequently fail to notice it has occurred. (Nitro’s law warns us that hidden precessions may be created by, and also the cause of many of the unusual effects, that we see, and some that we fail to see.)
This smooth occurrence of hidden precession(s) gives us the intuitive perception that precession is capable of changing directions without producing a significant counter-effect. (This is an error in perception.)
For example, when we torque a gyro system (to make precession move the gyro up), we don’t see a counter-action opposite to the direction in which the precession moves. (I.e. Precession moves the gyro up without a downward counteraction.) What we do see is a counteraction opposite to the direction in which the torque was applied.
Any other forces (no matter how gingerly or unknowingly applied), create counteractions, but we have difficulty perceiving them because our brain is accustomed to expecting counteractions to occur in a direction opposite to the new direction that we see the gyro going.
Example-2: The change in direction of precession caused by the drag of deadweight is easily NOT noticed because the deadweight also has the effect of increasing the force of gravity (though the acceleration of gravity is constant at 32ft/sec-sec, gravity’s force does change with the magnitude of the associated mass F=MA). This increased downward force distracts the true reason why the gyro moves downward at a slightly faster rate. We erroneously perceive the gyro as moving down faster (as if getting tired or dragged down) because the added weight is pulling it down. This is an error because (if anything) the stronger downward force should be providing precession with more energy. What is really occurring (and we fail to perceive), is that the sideways drag of the deadweight (though extraordinarily mild) is causing a very slow DOWNWARD PRECESSION to occur (the sideways drag presents an unperceived sideways force against the original precession, and creates a new modified direction of precession).
Some interesting initial experiments show that “accelerating” the downward force of a ‘gyro-on-a-tower’ (without use of a weight) actually causes the gyro to appear to temporarily ‘push-back’ upward (it behaves with an elasticity similar to pushing down on a piston full of air). These experiments are not controlled and their observations may not be clean enough to derive conclusions from. However, these crude experiments do demonstrate that the force from a weight has a slightly different effect than that of applying an increased acceleration. (At this point, I will not get into the role that “J” plays in these experiments.)
Q. Where does the energy for each change in direction of precession come from and where does the energy go?
A. The energy comes from the applied torque that is causing the precession in the first place, and it goes, in part, into the obstacle that causes the change in direction of precession.
Q. Will any of the energy become converted into linear forces, and if so, will any of those forces have an opposite reaction or not?
A. Yes, the energy absorbed by the obstacle should create a linear motion, and the opposite reaction causes precession to change directions at 90 degrees (you guess in which direction).
Q. Will the momentums infused by the resulting forces have inevitable encounters (somewhere in the cycle) that will nullify the created momentum? (Recall the “common flaw” illustrated by the “up-like-a-gyro and down-like-a-weight” design.)
A. No, there should be no motion that needs to be stopped at another place in the cycle, unless the impact causes a bounce-back that needs to be stopped at the end/bottom of the cycle (there is no indication that this will occur).
(Understanding the answers to these questions is important to the creation of thrust from precession.)
Designing Efficient Propulsion:
If we torque the system sufficiently hard (even though most of the torque is converted to precession) we can manage to budge the gyro into the direction of the applied force (i.e. into what appears to be classical motion).
How much of each torque applied on a system will result in classical motion Vs precession?
Are slower spinning gyros more likely to yield the classical type of motion when torque is applied?
Do faster spinning gyros respond with a larger proportion of precession and less classical motion, even though their precession occurs at slower velocity?
Can we predict the proportion of applied torque that will turn into precession as opposed to classical motion?
Laithewaite provided a single answer to all of these questions. His opinion was that the proportion of torque converted to classical motion is determined by the proportion of deadweight, and it is also possible that friction may contribute toward classical motion (when torque is applied to a gyro).
Knowing the proportion, of classical Vs precession motion, derived from given torques and spin rates can help to design more efficient mechanical propulsion devices.
Thank you, Luis
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| Answer: |
Luis Gonzalez - 04/06/2006 16:03:05
| | | Kinetic energy, Nitro’s law, and propulsion during impacts of precession
The very basic effects, that result when precession encounters an “object,” are not difficult to grasp and are easy to verify. Intuition and simple experiments show that some of the energy is transferred to the obstacle-object.
What remains in question is how to control and maximize the extent of the desirable energy transfers during the impact. That’s when it becomes necessary to understand the intricacies of the interactions of precession.
Can the forces resulting from the impact be harnessed, and if so, how efficiently? (What significant factors yield high levels of propulsion from the impact of precession?)
The Paradox of Spin Rates:
A) Should faster spin rate (which produces slower precession) transfer less energy to the object-of-impact in its path because of the reduced velocity of impact (caused by the slower precession)?
B) Inversely, should the higher momentum, stored in the faster spin of a flywheel, provide a stronger push against an obstacle that interferes/collides with the path of precession?
C) How does increased incidence of Nitro’s law (and its 90 degree wrapping) affect the transfer of energy force to the object that receives the impact of the collision?
Two types of conversion from PRECESSION’S kinetic energy occur during the impact in question.
Type1 - The impact creates a linear exchange of forces between the 2 objects involved and each object walks away modified (with a velocity of different magnitude and in a different direction).
Type2 - The impact creates a “SECONDARY direction of PRECESSION” (per Nitro’s law) upon the object that was moving in precession. The curling or wrapping motions, of the initial precession, transfer the bulk of the energy exchange back upon the spinning component of the system causing it to change its existing alignment dynamics. The new dynamics and realignment of the spinning component guide the direction of the secondary curvilinear motions.
Recall the intuitive theory of precession (that I presented earlier in this thread), which states that angular motions/forces induce other curling or wrapping angular motions (of similar type) and lead all of the attached spinning objects towards a balanced state so that all spins will eventually occur in the same direction and on the same or parallel axis (congruently).
The dynamics alluded to in a type1 conversion indicate that part “A” of “The Paradox of Spin Rates” carries more weight and we should pay attention to it. The fact that very fast spinning gyros produce precession of slow velocity, and that slow velocity generally contains a low level of kinetic energy can lead one to conclude that slower velocity precession may not transfer sufficient energy to produce a significant amount of propulsion. The answer to A is yes; therefore the solution to produce more propulsion appears to be in creating precession that moves as fast as it is technically possible to produce.
The dynamics of “Secondary Precession” presented in a type2 conversion (above) provide a complex answer to part “B” of “The Paradox of Spin Rates.” It indicates that angular momentum has a tendency to interact with and result in other forms of angular momentum in the objects that are spinning within the system. All other motions that result from it are secondary.
Curling or wrapping motions have a propensity to curl at 90 degrees and appear to do so more smoothly than when straight line motion changes direction. Intuitively one can visualize that the greatest part of the energy exchange, when a spinning object is forced to change direction, takes place in the object itself, where the spin is occurring; all other action is peripheral to the change in direction of the spin (of that object). Because of that, though we may perceive that the higher momentum of spin creates resistance to certain applied angular motions, higher spin rates do not transfer easily into curvilinear motions and forces. This is consistent with what we observe in experiments, and is one of the reasons that converting circular forces into linearly directed force is not a trivial matter.
The answer to Part “C” of “The Paradox of Spin Rates” is that objects moving according to Nitro’s law do not appear to lose or transfer a large proportion of their momentum as they curl into a new direction (i.e. the spinning object appears to maintain its magnitude of momentum albeit in a new direction). It is possible to see why a fast spinning gyro would sublimate a larger part of the kinetic (curling) energy, stored in its precession-motion, by following Nitro’s law into new 90 degree wrapping motions (unlike a linear motion governed by centripetal force into a curve). So the answers to items “B” and “C” complement each other. The important question to designers is; how to reduce the effects of Nitro’s law when precession encounters an obstacle that is intended to absorb as much energy as possible from the velocity of precession.
The theory indicates that adopting an appropriate rate of spin for the gyro flywheel(s) will maximize the linear force resulting from impact. The spin rate should maximize the velocity of precession and minimize the wrapping or curling into secondary precessions.
The fact is that many of the issues have been resolved but some challenges remain and here is a list of some of them.
1. Building the basic components accurately is challenging
2. Providing sufficient power to the moving components is not trivial
3. Providing the necessary changes of angular velocity quickly and in a nearly perfectly synchronized manner requires a light, strong and fast design
4. After an effective impact of precession, the cycle needs to return the flywheel back into position to initiate the next impact (this may present problems or an opportunity to capture a bit of extra secondary thrust).
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The content of this thread outlines a cohesive theory on how to use internal rotating components to produce linear propulsion.
It is the first such coherent theory in which each increment of linear velocity created is expected to survive the full completion of each cycle. Therefore it is also the first theory that states how to gradually buildup the linear velocity of the device (with each cycle delivering an additional increment of velocity).
Up to now, all other such theories have either been not complete or bring the linear velocity of the device to a full stop during the course of each full cycle. (Most of the “incomplete” theories claim unknown forces as the explanation for the intermittent occurrences of desired functionality and for unusual behavior or phenomena; that’s why they are incomplete theories.)
A major breakthrough of this theory is that it is cohesive and fully explained (within the realm of Newton’s physics). Only minor corollaries or observations need to be introduced; the first one is Nitro’s law, and the second one is that rotating objects seek to become congruent with the net angular direction of the torque applied.
Assuming the theory presented here is valid and based on correct premises, I estimate that executable building design plans may be completed in 4 to 8 months, and a working model should be completed for testing in 18 to 36 months. A successful test-model should liftoff from the ground and remain aloft for a time period greater than 3 times longer than if the device were tossed to the same height, plus the length of the device itself (this is important to account for the possibility of prolonged hang time due to re-location of internal masses; similar to the way basketball players appear to stay aloft longer than one would expect).
The theory contained in this thread is intended to permit any inventor (who is well versed in basic physics), to build a working device. The theory does not invoke any far flung concepts and is not based on any unproven high theories that require knowledge of esoteric facts or mathematics. Everything in this theory is down to earth but not necessarily trivial. The inventor that manages to build a working model from this theory will certainly require an agile, adroit mind and an ability to overcome a number of building challenges.
Thank you, Luis
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Luis Gonzalez - 22/07/2006 15:38:54
| | | To all enthusiasts who consider building prototypes according to the theory model described in this posting, the following will help in calculating the amount of thrust produced by your design.
It is critically important for a good design to understand the effects on thrust caused by the ratio of the mass of each gyro, to the mass of the device as a whole.
In other words, understand (quantitatively) what happens to the transfer of kinetic energy (energy of motion) during a fully elastic head-on collision of objects.
The ratio of the mass of the delivering object to the mass of the receiving object affects the amount of energy transferred in a NONLINEAR progression.
As a baseline, if the objects are of the exact same mass then the fully elastic collision will transfer 100% of the velocity (and kinetic energy) to the receiving object (assuming the receiving object has an initial velocity equal to zero).
The nature of our devices dictates that the mass of the receiving object (the overall device) will be greater than the mass of the delivering object (the gyro flywheel).
Though we try to maximize the mass of each gyro and to minimize the mass of the device as a whole (to the best of our ingenuity), their ratio is determined by a combination of materials, structure, etc.
To find out what happens as the receiving mass increases one need only make use of a very simple equation (there’s no need to wrap one’s brain around any mind boggling math).
Assuming the gyro collides with the device while the device as a whole stands motionless:
The resulting velocity of the receiving device (after the impact) is equal to twice the mass of the gyro, times the velocity of the gyro, divided by the sum of the mass of the striking gyro plus the mass of the device as a whole. (Simple)
The kinetic energy transferred to the device is equal to four, times the mass of the gyro, times the mass of the device, times the kinetic energy of the gyro, divided by the sum of both masses squared. (Not too difficult! Only need the kinetic equation.)
These are simple (and somewhat intuitive) relationships described by the appropriate physics equations that help to approximate quantification for this layer of the interactions.
For the mathematically inclined, the above relationships are described in the following expression where A is the gyro object and B is the device as a whole object:
VB2 = (2MA)(VA1) / (MA + MB)
&
KB2 = (4)(MA)(MB(KA1) / ((MA + MB)**2)
Note that we have not yet quantified, to what extent Nitro’s law reduces the transfer of velocity and energy from gyro precession to the obstacle in the way of precession’s path (i.e. to the rest of the device as a whole).
This reduction or loss of transferred energy may be calculated independently, or it may be integrated into the other calculations of kinetic energy that fails to be transferred to the device.
In a previous segment of this thread I addressed qualitative aspects on how Nitro’s law can reduce the transfer of kinetic energy.
The most significant component that contributes to Nitro’s factor (N) is the gyro’s rate of spin (this is important).
A quantitative calculation of the (N)-loss factor is based on knowing that, on one hand strong torque increases the “velocity” of both primary and secondary precessions (but does not increase the “propensity” of precession), and on the other hand when the force of the torque is increased, slower spinning gyros fall off towers (in a “classical” response) earlier than faster spinning gyros.
Intuitively, if slower spin is dominated by “classical” responses, then collisions involving slow spinning gyros should also be dominated by “classical” responses (at least, more so than faster spinning gyros). This observations point toward a somewhat gradual change from “classical” responses toward the phenomena we observe in precession, as the spin rate is increased.
On a subsequent upcoming segment in this thread, I will introduce plausible quantitative relationships, among some of the basic precession variables, which point toward how Nitro’s law may be quantified (I think this is an absolute need if we intend to fully understand how build our devices by design rather than by luck).
Thank you, Luis
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Luis Gonzalez - 06/08/2006 15:00:05
| | | Before quantifying Nitro’s law it is necessary to classify it.
Nitro’s law refers to the fact that dynamic systems produce many expected and unexpected forces that create precessions in expected and unexpected directions.
Nitro states his law succinctly and I hope he corrects me if I overstate or understate the law he has named.
There are at least 2 types of torque/force that can produce precession a la Nitro’s law (and otherwise).
The first type of torque is one from an “accelerating” force.
The second type of torque is one from a “decelerating” force.
There may also be a third type of force which simply modifies the direction of existing torques either in a subtle or radical way.
(They are all different shades of gray, of the same thing, “force.”)
These (2 or 3) types of intended and unintended forces are what Nitro’s law is about; some accelerate, others decelerate, and yet others modify the path of existing direction.
If these changes in motion were purely linear, then one could see them all as just “accelerations” by simply changing the frame of dynamic reference (some of you will recognize the basis of relativity, in this last sentence).
However, within a rotating system it is much more difficult (if not impossible) to jump from one frame of reference to another, in part, because we are forced to observe within the system, but mainly because a turning/spinning object can not be re-framed in a way that will make it appear as if it is standing still. A frame of reference that eliminates the spin would require the entire universe to spin instead (while with linear motion changing frames is easy).
This limitation in rotating systems brings meaning and importance to the difference between forces that cause acceleration, from forces that cause deceleration; it provides a mathematical symmetry.
Through this symmetry we can connect Nitro’s law to something, on the other side of the symmetry, that is easy to observe, and that is more familiar to us (though we don’t usually consider it useful).
This connection, of the difficult to see (Nitro’s law) with observations that we take for granted, opens the door allowing us to quantify Nitro’s law (and may even provide an equation, or two, for predicting the probability of when Nitro’s law will occur and how much thrust it may rob from our designs/devices).
What we find in the other side of the mathematical symmetry is “Drift” from precession.
Without further fanfare I will introduce the concept of “Drift” in precession (which may already be addressed in other theories by a different name).
“Drift” is what allows the force of torque (such as gravity or an artificially applied torque) to overcome precession.
I.e. while your gyro still has substantial spin, it is often overcome by the torque (e.g. of gravity) and moves down faster and, a bit later in the experiment, it falls off the tower.
At the same slow rate of spin (that the gyro falls off the tower), the same gyro in gimbals can still be forced into precession by a quick turn of the wrist!
So we must recognize that though precession still exists at lower spins, it is feebler and the gyro can be pushed around in the “classical” direction of the torque (this is “Drift”).
Many of us have observed this disappointing event, as our experiments wind down along with the speed of the gyro spin.
However, this is where the answers to Nitro’s law exist, at the fringes.
This disappointing portion of our experiments provides important information toward a theory that explains subtlety in gyro phenomena (in this case Nitro’s law).
At this point there may be an “AHA!!” in the mind of readers, or frustrated head scratching from others.
Moving forward, why is a gyro (at certain rates of spin) unable to stay on the tower but is still capable of precession when mounted on gimbals?
My answer is, mainly because of the rate of “Drift.”
I recognize that there are a number of other factors such as friction, imbalances, dead weight, etc, that contribute to “Drift,” but by themselves they are not sufficient to bring the gyro off from the tower at the point that this occurs.
In my opinion, the most significant portion of “Drift” results from the interaction of the force contained in the gyro flywheel and the force behind the system’s torque.
If this conjecture is correct and I can use it to quantify “Drift,” then I can also use it to quantify the propensity for precession and that is what Nitro’s law is about!!
This is not the first time that applying a mathematical symmetry has been used to advance the understanding of a theory.
On my next posting, we will see how this theory fares, and may actually quantify Nitro’s law!
Thank you, Luis
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Luis Gonzalez - 09/08/2006 02:03:30
| | | Nitro’s law is about the propensity of various multiple dynamics resulting in precessions (at 90 degrees) instead of resulting in classical responses.
My conjecture is that the propensity for 90 degree precession is not always 100% for all spinning gyros.
Rather, the propensity for precession is dependent on the ratio of the force of the gyro-flywheel to the force of the torque.
For the mathematically inclined: Propensity for precession = X = f / F
(Lower case letters represent variables of the gyro-flywheel, and upper case letters represent variables of the system.)
This ratio can be calculated by: the radius of the gyro-flywheel divided by the length of the gyro-axle (i.e. system radius), times the square of the number of turns of the gyro-flywheel divided by the square of the number of turns of the system.
This calculation can be performed by anyone without any level of sophistication in mathematics.
For the mathematically inclined here is what the equation looks like:
Propensity for precession = X = f / F = (r / R) (p ^ 2) / (P ^ 2)
(Mass is not included, with the assumption that m = M.)
The execution of this calculation provides a number “X” that is equal to the trigonometric TANGENT of the TRUE angle of precession.
The true angle of precession is what remains after “Drift” modifies the 90 degree angle of commonly accepted precession.
WHAT!? Am I saying that precession does NOT always occur at 90 degrees to the applied torque?!!
YES! That is exactly what I am saying!
Stable precession occurs at very near 90 degrees, which is what we observe most of the time.
However, “unstable” precession does not occur at exactly 90 degrees!
My conjecture:
A) Introduces the concept of “Drift” (observed in most gyro experiments)
B) Claims that “Drift” is a symmetrical inverse to the propensity for precession, i.e. Nitro’s law
C) States that the ratio of 1) the force in the gyro-flywheel and 2) the force in the torque, together yield the tangent of an angle that determines how much the “Drift” affects the angle of precession.
If my conjecture is correct, then we are one step closer to answering another one of gyroscopic behavior’s perplexing questions.
That question is “why does precession occur at 90 degrees?”
The answer is that precession does NOT ALWAYS occur at exactly 90 degrees, but rather precession maxes-out and plateaus at 90 degrees.
Precession is more stable as it approaches and becomes infinitesimally closer to the 90 degree mark (i.e. when the tangent derived from the ratio of the forces approaches infinity).
Can I backup my claims?
First lest exclude precession at angles that are greater than 90 degrees; precessions CAN NOT occur at an angle greater than 90 degrees! (Think about it.)
In which direction would precession move if it were greater than 90 degrees??
No matter in which direction the gyro moves, the angle is always 90 degrees or less!
Cap this off by the fact that the tangent of 90 degrees is equal to infinity, which can NOT be exceeded.
Regarding precession at angles less than 90 degrees: note that even when precession occurs at less than 90 degrees it eventually ends up at the same location as if it had moved at exactly 90 degrees; i.e. it will look like it moved at 90 degrees.
At all angles less than 90, precession will travel a slightly longer path, following the path of a helix instead of a direct curve to its destination.
Now, visualize precession, with a “Drift” in the direction of the torque.
It will in fact move at an angle determined by the combination of both 1) the angle of precession and 2) the angle of drift.
It will move in a direction that follows the sum of the 2 vectors. The gyro will NOT move at exactly 90 degrees to the torque, and will instead trace the path of a helix. (Can you see how this is so?)
Why did I choose the ratio f / F and not something else, and how do I connect this ratio to the tangent of the true angle of precession?
#1). I know that the force “f” in the gyro-flywheel is what’s behind the gyro’s momentum, and that make it the root cause for resistance to changing the position of the gyro-axle.
#2). I also know that the force “F” of the system’s torque struggles to change the position of the gyro-axle.
#3). Therefore, these 2 forces (“f” and “F”) struggle against each other at about 90 degrees (not in a head-on encounter).
#4). I also know that during stable-precession “f” is significantly greater than “F.”
#5). Take these 4 facts and view them from the perspective of the model framed by my “angular definition” of precession.
Though I did not think of the concept on my own, I did decide to use it as the contextual definition of precession.
In fact, I like the way that Victor Geere states it better than my own definition so instead of repeating the definition that I wrote earlier in this thread I am going to quote what he wrote on 18 July 2006 (Thread ID=598). Victor said “…the spin of the gyro aligned with the external force causes a path of least resistance. If the forces are not aligned it causes instability that only ceases once the forces are aligned.”
This basically states the motive and behavior of precession within the context of spin without having to depend on contortions using linear forces.
From here, it doesn’t take a great leap to see that if we push something that has initial motion, the initial motion becomes swayed in the direction of the push; in a similar manner if we torque something that has an initial spin, the initial spin also becomes swayed in the direction of the torque, or as Victor calls it “the external force.”
The “instability” that exists when the 2 forces are not “aligned” is what I have termed (in #3 above) as 2 forces struggling.
The explanation appears long because there is a lot to cover.
However, if you follow the facts as stated, there is no need for a leap of faith to see that 2 forces exist and that their interactions define the behavior that we see in gyro systems.
The attributes of these behaviors are:
A) Speed of precession
B) The path of precession
C) The potential energy in precession
D) How precession responds to (and with) other additional forces.
Though I believe the statements I make in this thread are true, their accuracy remain in question until fuller testing is completed.
This part of the model theory should be relatively simple to digest when compared to what’s coming next!
Thank you, Luis
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Luis Gonzalez - 13/08/2006 21:35:04
| | | Before getting into more complex concepts it’s important to nail down the basics of the model theory. The What, Why, How, and Which of Precession!
WHAT is Precession?
Precession is the “motion” that occurs as an object realigns its rotation axis, to the rotation axis of the torque applied.
WHY do these 2 axes of rotation have to realign?
Realignment of rotation axis occurs because the aligned position is the position where the sum of all the dynamics requires the least (minimum) energy and is therefore more stable.
HOW does the rotating object determine in which direction to move so it realigns correctly?
The direction of realignment motion (precession) occurs as a result of the encounter of 2 forces in different directions. The aggregation of the force vectors determines the direction toward alignment.
WHICH forces create the vectors that determine precession’s attributes?
An inventory of forces tells us that Centripetal / Centrifugal (CC) forces exist in 2 locations, 1) the gyro-flywheel, and 2) the system.
The direction of Centripetal / Centrifugal (CC) forces is radial in relationship to their respective centers of rotation. Note that each CC force is distinguished from an exact twin that would be created by rotation in the opposite direction.
Therefore the direction of the momentum in rotation gives the forces involved a sense of direction that can be said to be right / left handed or clockwise / counterclockwise, depending on the perspective of observation. The dynamics of each cycle maintain absolute and balanced sets of symmetries.
To produce linear motion, one must breech the absolute symmetry. Up to now, linear motion has been accomplished (fist time 1968 Italy), but so far it is only created within the confines of each discrete cycle. We are able to increment distance traveled through discrete hops, but so far no one has been able to increment the velocity so that each cycle aggregates to the total velocity! Therefore what is being produced is not useful propulsion.
What will it take to produce TRUE linear propulsion?
My perception tells me that some levels of symmetry can ONLY be breeched within each cycle, and that the symmetry breeched is also automatically restored (by the dynamics) before the conclusion of each cycle. That’s why, currently, velocity created during the cycle comes to a full stop by the end of that cycle.
We are currently able to capitalize on the 90 degree SYMMETRY of MOMENTUM (through precession), and this allows us to breech the symmetry of linear DISTANCE-TRAVELED outside of each cycle!
To truly breech a higher order of motion (velocity instead of distance) our devices must capitalize on a 90 degree SYMMETRY of FORCE. Accomplishing this higher level breech within the confines of each discrete cycle, should also allow a higher level of external breech (allowing external aggregation of velocity, not just aggregation of distance).
Does precession have 90 degree symmetry of force?
How can we find it, or induce it, and how can we use it?
These questions have already been addressed previously in this thread.
My next posting will be on the special case of precession under gravity, before moving on to the dreaded “probability angle distributions.”
Thank you, Luis
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Luis Gonzalez - 12/09/2006 23:31:37
| | | Precession results from how the laws of physics determine stable spin motion and how stability remains in the face of external forces interacting in non-intuitive ways. The scarcity of adequate information in this area of physics begs for a sense of organization starting with the easy basics and going on to the more complex. For that reason I have compiled a list of the things we know intuitively about circular motion and from that build up gradually until we encounter precession in a logical manner. This may or may not be the first time these points have been organized and developed in this manner, but than we all do things in different ways.
Starting with the simple basics, we will look at the properties of spinning objects, purposefully avoiding the configuration of a gyro on a tower under gravity (which we will cover later).
Rules of Stable Spin:
#1 - The center core of the spin-axis is generally the least dynamic.
#2 - Objects (including a disk) can spin around ANY axis of symmetry (i.e. any axis that distributes mass symmetrically).
#3 - Masses outside the center of spin tend to continue in a straight line motion (per Newton) and are kept in check by the centripetal force imbued by the cohesive forces of the material. The centrifugal effect causes larger mass to preempt the outer perimeter of spin, depending on the geometric shape of the object.
#4 - The most stable axis of spin has the highest symmetry, and/or provides the longest spin radius to the largest proportion of mass, symmetrically (consider a disk).
#5 - Depending on its geometrical shape, an object spun around multiple different axes will settle into a spin-axis that is either, a) the average of the different axes of spin, or b) the sum of the spin-vectors, or c) an axis that conforms to the most suitable axis of spin as stated in rule #4 above (consider a disk).
#6 - An object in a stable spin-axis tends to stay in that configuration even if other spin-axes configurations of greater stability exist. The reason is that to change its spin-configuration from one stable spin-axis to another stable spin-axis, the object needs to cross fields of configurations that have highly unstable spin-axes.
#7 - To induce a switch among stable axis configurations requires an external force of sufficient magnitude applied in the appropriate direction.
#8 - As long as the torque-axis “precedes” i.e. continues to exist ahead of the spin-axis, precession continues to occur (as soon as the 2 axes are lined-up parallel, precession stops).
These (maybe incomplete) set of rules explain how objects can spin and can settle into one of many stable spin axes with different levels of stability. A coin twirling on a smooth surface illustrates how a disk is able to spin on an axis of symmetry that is not optimal for a disk (as compared to the spin of a gyro, which spins on the main axis and is in an optimal spin configuration for a disk.)
Gyro flywheels happen to spin in the most stable axis-configuration (for a disk) because they spin on the axis of highest symmetry that also provides the longest spin-radius to the largest proportion of the mass of the disk (per rule #4 above). These 2 factors provide a strong deterrent to change from a highly-stable spin configuration. Well balanced gyros in a stable spin can self-correct most induced wobbles.
Note that change to a stable configuration can be induced by a sufficient external force applied in the appropriate direction. For example, a spinning disk may be made to wobble by introducing a specific type of interference. The cause of a wobble can be of sufficient magnitude and/or can have a harmonic resonance capable of changing spin-axis configurations (e.g. frictions or imbalances can produce destructive harmonic frequencies).
Some of us may perceive that the existence of multiple spin-axes, each with a different level of stability, represent different energy levels (food for thought).
Here comes what I believe to be an innovative view of precession’s root cause (the why & how). The tendency to maintain stable configurations of spin is (probably) the most significant contributing factor to what we know as “precession.” The dynamic self-correcting state of spinning disks make gyros under torque, change orientation in order to maintain their configuration of high order spin-stability (is this statement new?).
Consider that an external torque attempts to change the spin-axis configuration of a disk to a spin-axis of lesser stability. To visualize how this is so, think what the same torque does to a non-spinning gyro; it makes the disk twirl like a coin twirling on a smooth surface. However, in a spinning gyro, the spin-axis would have to cross fields of high-instability in order to reach the relatively less stable “twirling-type” of spin.
When an applied torque attempts to introduce this (coin-like) twirling-type of spin to an already spinning disk, it attempts to both, twirl (on a lesser-stable-axis) and at the same time spin about the main axis of the disk. This extremely chaotic motion is highly-unstable and would violate many rules of spin. (Note - The chaotic motion is not necessarily impossible, but would require the disk to exist in an axis of highly complex symmetry and dubious stability, which theoretically needs a different level and sort of energy).
Therefore, in absence of unusual, strong types of energy, the torque applied to a spinning gyro will cause the disc to respond by repositioning itself into an orientation that allows it to maintain the highest symmetry of its original spin-axis configuration.
The only way the gyro can maintain this original stable spin-axis is by “following” the spin-pattern of the torque, and making its spin-axis parallel to (or the same as) the spin-axis of the torque (through changing axis-orientation rather than changing its axis-configuration). In other words, the spinning disk will seek the position where the direction of the torque is congruent with the direction of stable spin (i.e. where their spins are in the same plane and their axes are parallel or the same). Most important, a gyro’s degrees of freedom allow for a change in orientation for the spin-axis, and THIS BEHAVIOR IS AT THE CORE OF PRECESSION!
In case you missed the meaning of my explanation, symmetries of mass dictate an object’s stable-spin configurations, and gyros have sufficient degrees of freedom to adjust their orientation so that they can maintain a stable spin-configuration when an external force/torque attempts to disrupt the stability. These concepts appear initially complex but become simple with time and familiarization.
This rational development of ideas, starting with commonsense reasons for how spin occurs, followed by spin’s interactions when coupled with external forces within a gyro’s degrees of freedom, is the basis upon which my definition of precession is built; the resulting theory model is consistent and based on premises that can be proven.
With this basic understanding of rules surrounding spin, we may take a fresh look at my basic explanation of precession, and to how it extends to the behavior of the familiar toy-gyro (which has an asymmetric axle, gyro-on-a-tower under gravity configuration). So let’s start by exploring the meaning of the word “precession.”
Roget’s Thesaurus associates the word, “precession” with “precedence” meaning previous-ness; and with “preceding” meaning to lead or to go in front of something. It appears that ‘precession’ describes how the “torque-axis” relates to “the spin-axis” in the dynamics of gyros; i.e. the torque-axis always precedes the spin-axis during precession.
I have explained elsewhere that the toy gyro configuration (on a tower under gravity) derives its ability to continue rotating (beyond 180o) from the inability of the spin-axis to ever catch-up with the torque-axis (derived from gravity). As precession moves the toy-gyro around horizontally, the pivot-axis (which is derived from the axle resting upon the tower plus gravity) also moves around horizontally. Thus the torque which results from the pivot (gravity pulling down on the gyro side of the axle while the tower maintains height on the other end of the axle), also moves horizontally. Since both axes move horizontally, at the same rate, and in the same direction, the spin-axis never catches-up with the torque-axis; hence they remain orthogonal (clear?).
This “eternal” chase is proper only to the toy-gyro (under gravity). In contrast, the spin-axis of gyros with mechanically induced torque (e.g. in gimbals) manages to catch-up with the torque-axis (always) within 180o span of angular precession (see Victor’s drawing).
A question has been raised whether we should call the 90o motion induced mechanically on a gyro (e.g. on gimbals), by a different name rather than precession! Though this motion is independent from gravity, it also occurs at 90o to the torque applied and relies on the exact same basic mechanics. The main difference is that the device with mechanical torque (e.g. a gyro in gimbals receiving a twist to the outer cage) produces a motion at 90o in a way that the spin-axis can catch-up to the torque-axis! In other words the gyro re-aligns the orientation of its spin-axis (NOT the configuration) until it gets to a stable position (as illustrated by Victor Geere’s drawing, when both axes lineup). Once both axes lineup the torque-axis ceases to precede or lead (as opposed to the toy gyro), and the 90o precession motion also STOPS. Rule #8 says that as long as the torque-axis “precedes” the spin-axis precession continues to occur (as soon as the 2 axes are lined-up parallel, precession STOPS).
In a strict sense, the 90o motion caused mechanically (e.g. gyro in gimbals) is indeed as much a form of precession as the one created by gravity for the following reasons: 1) Both motions result from the same type of interactions between torque and spin. 2) Both motions follow the same rules of physics. 3) Both motions occur at 90o to the applied torque. 4) Later we may see that both motions also occur at 90o to the spin of the gyro flywheel.
These 4 points apply to the 90o motions of precession in toy gyros as well as to the 90o motion of gyros in gimbals; both come from, and follow the same rules.
In my opinion both 90o motions are the same with a difference in the mounting configuration due to the use of gravity as the source of torque, versus the use of mechanical torque.
Therefore, the word “precession” is appropriate to describe all 90o motions that result from interactions of spin with torque (what else would you call it and why?).
In the same way, since it is the “acceleration” of gravity which creates the force for the torque, I don’t agree to use the term “accelerated” to differentiate mechanically driven torque, because all torque is always derived from “acceleration” whether it is mechanically induced or from gravity.
Other individuals argue that the word “precession” should only apply to gyros under gravity. This creates an artificial break in the language used to describe precession. The resulting, discontinuity to the flow of thoughts, creates a block to understanding and prevent explaining the root causes of precession.
If we want to eventually bring some clarity to the subject, I say it is wiser to stick to unequivocal terms. The subject is complex enough without adding unnecessary ambiguity. We can use existing, well known, well defined terms and differentiate them with appropriate qualifiers if we need to. I bring this up because complexities are difficult by definition, and creating ambiguous terms can only add obscurity and perpetuate widespread ignorance of the subject.
Admittedly, the facts contain numerous interrelated details and this makes the subject difficult to address in a quick easy manner. Sticking to correct appropriate terms allows easier connection of the many facets, and permits at least a few bright and dedicated individuals to eventually break through and understand.
(Excuse me before I fall off my soap-box as I get on my high horse.)
I believe that this posting (in conjunction with others) completes a comprehensive (though not concise) explanation of precession’s behavior including causes and effects, from a perspective of classical physics.
Good science does not need to state the “what is” of a phenomenon; good science needs only explain the “how” in a way that permits quantification and/or establishes acceptable connections to previously proven, accepted rules.
Any fuzziness in making these connections may bring into question the style of writing, the person writing it, and the choice of forum for that matter. However, dedicated bright individuals with a fair understanding of real physics will eventually decipher that the facts are correct and stated in consistent language. Brighter individuals will infer how knowing these facts allow one to prescribe measurements and verify the coherence of the model theory. It may take some time (all good things take time), but time will tell.
I have yet to find as complete a layman’s explanation for precession, as is stated here. In contrast, one of my college physics books explains precession using a rule-of-thumb (literally) interpretation of angular accelerations. Though the explanation in that book is a bit ridiculous, it does make use of the same rule of thumb used by electric engineers and, right or wrong, appears to create a faint connection between the two fields.
I feel that I have conveyed a perspective of how I see precession occurring as a result of known intuitive interactions. These explanations are better understood from the perspective of a gyro in gimbals, where the acceleration for torque is produced mechanically, and not by gravity (this configuration provides a simpler model with fewer variables).
I have, elsewhere explained how these interactions that occur on the gyro-disk, can project their effects into a motion of translation that causes toy gyros to revolve (like a planet). Therefore I will leave that explanation for the readers to find among my other writings, if they wish to complete those pieces of the puzzle.
Basically, precession in a gyro-on-a-tower configuration results from an interaction of forces that occur on the gyro disk, not at the center of rotation. In the tower-configuration, planetary-style precession is driven from the gyro mass at the perimeter. The center of rotation of the system does not provide direct drive force to the planetary-style motion of precession; the center of the system only provides a pivot point.
Thank you, Luis
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Luis Gonzalez - 03/11/2006 16:37:45
| | | The most interesting behavior of gyroscopes is observed in the common configuration of the gyro on a tower, but the doorway to discovering true linear gyro-propulsion (Vs linear-motion) is hidden in the intricacies of what takes place within only the gyro-flywheel itself.
The path to knowing how to create true gyro-propulsion is in knowing how to accurately map the dynamics taking place on the flywheel disk, and connecting them to the revolving “displacement” motion of the disk mass around the (less massive) pivot center (i.e. knowing why the system’s precession turns on a pivot point other than its center of gravity).
Consider the following points:
* The length of the gyro-axle (the system radius = R) has no effect on the cycle rate of precession; i.e. the length of “R” has no effect on the angular velocity of precession measured in radians. All else being equal, changing the length of the gyro axle (R) does not affect the rate of precession cycles.
* We know that torque (T) is equal to force (F) applied, times the Radius of the system (T = F x R, where R = length from gyro-flywheel to pivot point). If the “R” component of torque has no effect on the cycle rate of precession, then the cycle-rate of precession is entirely dictated by the force (F) component of the applied torque and by the parameters of the gyro-flywheel such as the spin rate and its radius (r). (The mass also cancels out because it is in both the numerator and the denominator of the equation for precession.) This means that the radius (R) component of torque is important only to find the length of the distance traveled by precession (I think that’s very interesting).
So what?
This means that the gyro’s precession cycle rate is the same despite the length of the pivot axle (R), or even if there is no pivot axle, as long as the “torque” force can be applied. The implication is that the dynamics that cause precession are ENCAPSULATED entirely within the parameters of the gyro-flywheel; the behaviors and phenomena in the rest of the system are induced and ultimately entirely dependent upon the parameters on the gyro-flywheel, and how these parameters respond the induced acceleration of the applied torque. One may see this encapsulation as a benefit, because it focuses the initial attention of developing a theory purely on the gyro-wheel, and one need not initially consider the more complex phenomena that result when an extended axle is added to the configuration; extending that axle generates revolving motion which “displaces” the gyro’s location from one place to another (this is what we see as precession in a gyro on a tower).
Once we determine rationally and intuitively that the dynamic source of precession originates at the gyro-flywheel, we become able to make other great discoveries. One of these great discoveries is that the Centripetal/Centrifugal (C/C) forces in the motion of precession also take place ONLY at the gyro-flywheel level (NOT at the system level)!!!
In other words, the motion that displaces the gyro (e.g. gyro on tower) has no C/C forces because C/C forces reside in the gyro-flywheel’s re-orientation motion, not in the displacement motion.
Interestingly, the C/C forces of precession within the gyro-flywheel are much smaller than C/C forces of spin in that same gyro-flywheel because the spin-rate is generally faster than the precession-rate. Therefore the C/C forces of precession are easy to miss or to ignore altogether. These last facts provide a lot to think about; we may discuss some of these thoughts in future occasions.
To reiterate, the great thing about this analysis is that, up to a point, it explains why one can’t find C/C forces in the revolving “displacement” motion which occurs in precession on off-center gyros (e.g. gyro on a tower); the reason is that the C/C forces of precession reside on the change in orientation of the gyro-flywheel and not in the change in location of the flywheel. That is a simple and elegant answer to a vexing question!!
That said, its very important to note that revealing these facts does NOT in any way imply that the revolving “displacement” caused by precession is void of momentum; on the contrary the revolving “displacement” motion caused by precession does indeed carry momentum (MxV) that may in some occasions be greater than the momentum resulting from revolving the mass of a gyro-wheel when it is not spinning (i.e. not in precession). Can you see how this is so?
There are a couple of factors that hide the strong momentum in the revolving “displacement” motion of precession. One of these factors is a gyro’s tendency to respond to OTHER interactions, by moving in new directions of (secondary) precession (Nitro’s Law). Other such significant factors exist but I do not wish to discus yet.
A question whether precession affects the velocity of spin also has been raised without a satisfactory answer. The following may provide an intuitive perception that may lead to an answer: If one adds the vector of precession’s motion to the vector of spin, than one can see how precession increases the net motion of the particles at the rim of the gyro-flywheel. However this does not mean that the gyro is spinning any faster, but simply that the sum of all the gyro’s motions is increased.
Back to analyzing the causes of precession, thanks to Momentus for introducing the concept of “couple” and how it relates to precession. His explanation of precession in terms of a “couple” (an interaction of parallel forces) has in part brought a deeper intuitive understanding of what takes place within the gyro-flywheel. I can’t improve upon Momentus’ words stated in this forum at “http://www.gyroscopes.org/forum/questions.asp?id=350.” I will leave it to the capability of each individual to figure out where and how Momentus explains precession in terms of “couple.” (This may be for advanced members, but I am not certain.)
Now, one of the best hidden secrets of nature is how the precession dynamics on the gyro-flywheel can cause the revolving “displacement” that we see in the usual gyroscope configuration, i.e. how it displaces mass from one location (around) to another. This displacement occurs without creating a significant reaction at 180 degrees, and that is another interesting point (besides the apparent lack of C/C forces). Let’s start with a quick explanation for motion of precession without apparent equal and opposite reaction (at180 degrees). The reason is that the reaction to precession occurs in response to the applied torque, which was also applied at 90 degrees to the resulting precession. The torque and the equal and opposite reaction (counter-torque) maintain their classical 180 degree relationship; however the action resulting from the torque occurs at 90 degrees and is “precession.”
The relationships among torque, counter-torque, and their resulting paired motions have a tendency to become confused when we look at precession.
Back to the main point; how does the revolving “displacement” motion of precession come to happen if all the dynamic result takes place within the gyro-flywheel (including the C/C forces)?
The simple answer is that the flywheel’s force (couple?) to reorient itself, in precession, does so even if it is required to transport its mass, displacing it from one position in space to another (through the revolving motion).
Let’s explore this idea:
A gyro mounted on a pivot point via an off-center axle, has its DEGREES OF FREEDOM moved or relocated to the pivot-point positioned at the other end of the axle. It is the location of the degrees of freedom that now exist at the distant pivot point (but not the C of G which has been erroneously suggested previously in this forum). By implication, the degrees of freedom are no longer viable at the C of G of the flywheel, because the flywheel is attached to the rigid mechanical axle. Does this shed a small ray of intuitive light upon the dynamics that take place in this more complex configuration? Does it explain why the revolving motion caused by precession does not have C/C forces but still carries momentum (without need to invoke deep MYSTERIOUS forces)?
One more thing, the concept of circular motion without C/C forces is not entirely unique to precession. A mass attached at one end of a rigid arm whose other end is attached to a central pivot can be forced to travel along the perimeter by applying a force at a bit over 45 degrees to the tangent of the circular perimeter, where the mass resides. If the force can be maintained at the same approximate 45+ degrees (by moving the force along with the mass), then the resulting circular or angular motion exists without C/C forces. The turning motion that results does not require pulling-in by the substance of the radial arm (i.e. does not require Centripetal force). Also, the mass in motion would not tend to continue in a straight tangent line if the radial arm were destroyed (i.e. does not have Centrifugal action); in such event the 45+ degree force would tend to implode the mass toward the general vicinity of the circle’s origin. This is not the normal behavior of common angular motion which displays result of C/C forces.
Here is another interesting experiment of angular motion without C/C forces: Take a rigid-arm pendulum capable of full freedom to move all the way around 360 degrees on a bearing. Hold the pendulum weight at the 12 o’clock position and then let it go. The first few degrees of motion have negative C/C forces until the mass travels past around a 45 or 90 degree arc. Then there is a short span of arc where C/C forces are at zero, after which the pendulum acquires relatively normal C/C forces.
This simple experiment illustrates that anomalies may not be as rare and mysterious as we first think. Can you think of other such instances?
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