Moment of inertia

Question

A wagon wheel is a thin metal ring

of mass 57.1 kg and radius 0.530

m. What is its moment of inertia?

[?] kg-m²

can someone please answer this thourghly ?

Answer 1

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:

I=mr²

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:

I=∑mr²

The radius is constant, so this can be simplified to:

I=r²∑m

And we know that ∑m is the sum of all the mass, or the total mass, which we can denote as M. Therefore:

I=Mr²

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=Mr²

I=(57.1 kg)(0.530 m)²

I=16.04 kg·m²