Chapter 12, Problem 4A

Which has a greater rotational inertia, a cylinder about its axis or a sphere about a diameter if the two have the same mass and radius?

To determine

The shape that has the greater rotational inertia out of the cylinder about its axis or a sphere about a diameter if both have same mass and radius.

Answer to Problem 4A

Cylinder

Explanation of Solution

Introduction:

Rotational inertia of a uniformly distributed mass $m$ is given by,

  $I={\displaystyle \sum _i{m}_i{r}_i{}^2}$

Where, $r=$ distance of the considered mass elements from the axis of rotation is given by

As can be seen from above that the rotational inertia of an object is directly proportional to the mass of the object and to the square of its distance from the axis of rotation..

Now, in the cylinder mass is distributed at a larger distance from its axis as compared to the case in sphere.

Conclusion:

Hence, the cylinder has greater rotational inertia about its axis as compared to the sphere about its diameter.