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 is proportional to the distribution of mass about the axis of rotation. For the given objects, the solid sphere has all of its mass distributed uniformly around the axis of rotation, resulting in the least rotational inertia. The hollow sphere has a greater rotational inertia than the solid sphere because some of the mass is further from the axis of rotation. The flat disk has a greater rotational inertia than the hollow sphere because its mass is further from the axis of rotation in the z direction. Finally, the hoop has the greatest rotational inertia because all of its mass is at the maximum distance from the axis of rotation in the z direction. Therefore, the correct order is 1, 3, 2, 4.

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