Answer to Question #138922 in Classical Mechanics for dwight

Question

Which of the following has the largest moment of inertia?
A. A cylinder of mass M with a radius R rotating about its central axis.
B. A hoop of mass M with a radius R rotating about the axis perpendicular to the plane of the hoop and passing through its center.
C. A hoop of mass M with a radius R rotating about a line through its diameter and parallel to the plane of the hoop.
D. A cube of mass M and sides 2R rotating about a line passing through the center of two opposite sides.
E. A rod of mass M and length 2R rotating about a line passing through the center and perpendicular to the rod.

Answer 1

Solution

(B)  A hoop of mass M with a radius R rotating about the axis perpendicular to the plane of the hoop and passing through its center has largest moment of inertia. It's moment of inertia is given as

$I=MR^2$

Which is larger then other.