Question

Two spheres have the same radius and equal mass. One is made of solid aluminum, and the other is made from a hollow shell of gold. The axis of rotation for the solid sphere is at the rim, and the axis of rotation for the hollow sphere is through the center. Which one has the bigger moment of inertia?

Answer 1

By definition the moment of inertia is described under the function

`I= mL^2`

Where,

m = Mass

L = Distance to the center of mass

The moment of inertia is proportional to both bodies and as we can see, there is no change in mass, so

`I \propto L^2`

If the distance of the body is greater than the center of mass or the axis of rotation, its moment of inertia will be greater. In this case, the solid sphere has a greater mass than the hollow sphere. In addition, its axis of rotation is further away from its center of mass. Therefore by proportionality your moment of inertia will be greater.