Question

4) T F If two objects have the same moment of inertia, they must have the same mass.

Answer 1

Answer:

False

Explanation:

The moment of inertia for a rigid body is given by

$I=\int \rho(r) r^2 dV$

where

$\rho(V)$ is the density distribution of the object

r is the distance from the axis of rotation of the object

Essentially, the moment of inertia does not depend only on the mass of the object, but also on its shape. For example: for a solid cylinder, the moment of inertia derived from the formula above is

$I=\frac{1}{2}MR^2$

where M is the mass of the cylinder and R is its radius. As we see, I (moment of inertia) does not depend on the mass only: therefore, if two objects have same moment of inertia, this does not imply that they also have the same mass.