Gyroscope Math Page

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Notes and Reference Section

Basic Gyroscope Measurements
Density of material
Radius (Meters)
Diameter (Meters)	(Radius * 2)
Circumference (Meters)	(2 * Radius * Pi)
Depth (Meters)
Volume (Meters Cubed)	(Pi * (Radius ^ 2) * Depth)
Mass (Kilograms)	(Volume * Density)
Pi
Cut-Away Measurements
Radius (Meters)
Diameter (Meters)	(Radius * 2)
Circumference (Meters)	(2 * Radius * Pi)
Depth (Meters)
Number of Cut-Aways
Volume of Cut-Aways (Meters Cubed)	(Pi * (Radius ^ 2) * Depth)
Mass of Cut-Aways (Kilograms)	(Volume * Density)
Gyroscope Measurements (After Cut-Aways)
Volume of Gyroscope (Meters Cubed)	(Gyro volume - cutaways)
Mass of Gyroscope (Kilograms)	(Gyro mass - cutaways)
Inertia
Gyroscope Inertia (without cut-aways)	(Mass * (radius ^ 2) / 2)
Inertia Cut-Aways	(Mass * (radius ^ 2) / 2)
Omega (Gyroscope interia after cut-aways)	(without cutaways - cutaways)
Speed of Gyroscope
W (radians per second)	(rps * ((2 * pi))
Revolutions Per Minute (RPM)
Kilometers Per Hour (KPH)	(((rpm * circumference) / 1000) * 60)
Degrees Per Second	((rpm * 360) / 60)
Revolutions Per Second	(rpm / 60)
Speed of Main Structure
Degrees Change
Time in seconds
Radians Change	(degrees / (360 / (pi * 2))
Degrees Per Second	(degrees / seconds)
Revolutions Per Second	(dps / 360)
Revolutions Per Minute (RPM)	(rps * 60)
Omega (Radians per second)	(rps * ((2 * pi))
Details of Precession
C (Gyroscopic couple force)	(Inertia * W * Omega)
Force
Distance between bearings (Meters)
Force on bearings (Newton Meters)	(C / L)
Force on each bearing (Newton Meters)	((C / L) / 2)
Force on bearings (Kilograms)	((C / L) * 0.1)
Force on each bearing (Kilograms)	(((C / L) * 0.1 aprox) / 2)