We are asked to find the moment of inertia of a thin ring. We can derive this formula using the moment of inertia of a single particle:
Since the moment of inertia of a ring is the sum of many small particles at a constant radius r, we can find that the moment of inertia of a ring would be:
The radius is constant, so this can be simplified to:
And we know that ∑m is the sum of all the mass, or the total mass, which we can denote as M. Therefore:
for a thin ring of radius r and mass M.
Using this formula, we can get for a thin ring of mass 57.1 kg and radius 0.530 m:
I=(57.1 kg)(0.530 m)2