Chapter 12, Problem 19A

Three iron shapes of the same mass rotate about the axis shown by the circle with the dot inside. Rank them, from greatest to least, in terms of the rotational inertia about this axis.

To determine

The rank from the greatest to least rotational inertia about the given axis.

Answer to Problem 19A

  $C>B>A$

Explanation of Solution

Introduction:

The more the distance of the mass’s concentration from the axis of rotation, the more is the rotational inertia of the object.

Considering the above fact, the maximum mass is concentrated near the axis of rotation for the case A. And, thereby it will have the least rotational inertia.

Similarly, for the case C, the maximum mass is concentrated at the farthest distance from the axis of rotation. Hence, it will have maximum rotational inertia out of the given cases.

Conclusion:

Hence, the rank of the rotational inertia from greatest to least is $C>B>A$ .