Consider four objects, each having the same mass and the same radius:
1. a solid sphere
2. a hollow sphere
3. a flat disk in the x,y plane
4. a hoop in the x,y plane
The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:
A) 1, 2, 3, 4
B) 4, 3, 2, 1
C) 1, 3, 2, 4
D) 4, 2, 3, 1
E) 3, 1, 2, 4

Question

Consider four objects, each having the same mass and the same radius:
1. a solid sphere 
2. a hollow sphere 
3. a flat disk in the x,y plane 
4. a hoop in the x,y plane 
The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is: 
A)  1, 2, 3, 4 
B)  4, 3, 2, 1 
C)  1, 3, 2, 4 
D)  4, 2, 3, 1 
E)  3, 1, 2, 4

Quizplus · Accepted Answer

The rotational inertia of an object depends on both the mass and how that mass is distributed around the axis of rotation. In this case, all four objects have the same mass and radius, but their mass distributions differ. 
1. The solid sphere has its mass distributed uniformly throughout its volume, so it has the lowest rotational inertia of the four objects.
2. The hollow sphere has its mass concentrated in a shell around the center, so it has a higher rotational inertia than the solid sphere.
3. The flat disk has all of its mass concentrated at the same distance from the axis of rotation, which results in a higher rotational inertia than both the solid and hollow spheres.
4. The hoop has all of its mass located at the same distance from the axis of rotation, but none of its mass is located near the center of the hoop. This results in the highest rotational inertia of the four objects.

Therefore, the order of increasing rotational inertia is 1, 3, 2, 4, which corresponds to choice C.

Consider Four Objects, Each Having the Same Mass and the Same