Moment of Inertia and Frequency of Oscillation

UKDv12

How do you calculate the moment of inertia given frequency of oscillation?

sambristol

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 [itex]\pi[/itex] f) you have solved the problem

Hope this makes sense and helps

regards

Sam