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The Gyroscope Forum |
21 November 2024 21:53
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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: |
Harvey Fiala |
| Subject: |
Calculate Precessional Angular Velocity |
| Question: |
TAKE HOME QUIZ #1
For those who profess to fully understand the physics of a precessing gyroscope, here is a short take-home exam:
The basic equation governing gyroscopic motion is: T=I ωs ωp where T is the applied torque, I is the Angular Momentum of a rotor, ωs is the angular velocity of a rotor R, and ωp is the angular velocity of the resulting precession. Assume natural precession where the torque T is provided by the force of gravity at the surface of the earth and ωp is the resulting natural precession in the horizontal plane. [s and p are supposed to be subscripts to ω. Likewise in the following paragraphs, 1 and 2 are supposed to be subscripts to L, R, ω and I]
Assume a spin axis having a length of L1 from the pivot point with a rotor R1 having an angular momentum I1 and an angular velocity ωs1 . Now further assume that the spin axis is extended and is actually longer for a total length of L2 and that another rotor R2 at the length L2 has an angular momentum I2 and an angular momentum ωs2 .
It may be assumed that rotor R1 alone on a spin axis of length L1 would have a precessional angular velocity of ωp1 and that R2 alone on a spin axis of length L2 would have a precessional angular velocity of ωp2 .
Now we have a single spin axis or lever arm with two different rotors, each having a different angular momentum, angular velocity, and distance from the pivot point. Assume that both rotors are spinning in the same clockwise direction and are precessing in the horizontal plane and that the spin axis has negligible mass. What is the resulting precessional angular velocity ωp in the horizontal plane due to the force of gravity of the two spinning rotors on the one axis? _________
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| Date: |
9 September 2004
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