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 \pi f) you have solved the problem

Hope this makes sense and helps

regards

Sam