# Effect of gravity on the precession rate of a gyroscope

1. Jan 26, 2009

### em2390

1. The problem statement, all variables and given/known data
A certain gyroscope precesses at a rate of 0.60 rad/s when used on earth.
If it were taken to a lunar base, where the acceleration due to gravity is 0.165 g, what would be its precession rate?

2. Relevant equations
Is the precession rate directly proportional to the gravity exerted on it.

3. The attempt at a solution
Pr=Precession rate we know is Torque/Angular Momentum. The only place i see gravity is in torque (r*ma) so I figured that if the force of gravity is .165 times less, the PR would be .165 times less, or .60 x .165 = 0.099, but that's wrong

2. Jan 27, 2009

### chrisk

For large L the precession is proportional to the acceleration of gravity and independent of the angle of tilt.

$$\omega_p=\frac{mgr}{L}$$