(adsbygoogle = window.adsbygoogle || []).push({}); 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 ofR=1cmfrom the center of mass. The Gyrocompass is rotating with10 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 itsmoment of inertiashould 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 shouldn`t be correct, because the effect of the Earth angular moment isn`t 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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# Angular momentum of a gyrocompass

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