## Moment of Inertia and Frequency of Oscillation

How do you calculate the moment of inertia given frequency of oscillation?
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 You are going to need more than just the frequency. You will need to know the restoring force. I think the problem you are describing is a body hung on a pivot through a point on it and the body is displaced by a small angle θ with gravity acting on the centre of mass to restore equilibrium. In the limit of small θ the body executes simple harmonic motion. For angular displacements the equivalent of F=ma is τ = I d2θ /dt2 where τ is the torque about the pivot of gravity (mg) acting at the centre of mass and I is the moment of inertia about the pivot. Put this together and use the approximation sin θ ≈ θ for small θ and as you would for a simple pendulum solve to find ω (= dθ/dt) since ω (= 2 $\pi$ f) you have solved the problem Hope this makes sense and helps regards Sam

 Tags frequency, moment of inertia

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