# Angular momentum of a gyrocompass

1. Dec 10, 2009

### substance90

1. The problem statement, all variables and given/known data

I have a gyrocompass with a fixed axis at an angle alfa to the rotational axis of the earth. Omega "Erde" is the angular momentum vector of the earth and Omega K is accordingly of the gyrocompass.
The whole mass of the gyrocompass (m=0.1kg) is concentrated on the edge at a distance of R=1cm from the center of mass. The Gyrocompass is rotating with 10 000 RPM.

I have to calculate the torque induced in the gyrocompass by the angle to the earth rotational axis.

2. Relevant equations
I guess that because of the form of the gyrocompass its moment of inertia should be I = m*r^2

Angular momentum = I*omega
Torque = I*omega'
Omega K = 2*pi / T
T (Period) = 60/10000

3. The attempt at a solution

I tried calculating the Omega Z component of the angular momentum of the gyrocompass with Cos(alfa)*Omega K, which I find via the moment of inertia and RPMs. Then I calculated the torque using only the Omega Z component, but that shouldnt be correct, because the effect of the Earth angular moment isnt taken into account and conservation of angular momentum, too.

Any ideas would be greatly appreciated! By the way this is pretty urgent, I have to have it ready by tomorrow!

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Last edited: Dec 10, 2009