A solid sphere,a solid cylinder,and a hoop each have the same mass and radius.If they are spinning at the same angular velocity,which one has the greatest angular momentum?
A)the sphere
B)the cylinder
C)the hoop
D)They all have the same angular momentum.

Question

Quizplus · Accepted Answer

The angular momentum of a rotating object is given by L = Iω, where I is the moment of inertia of the object and ω is its angular velocity. The moment of inertia of a hoop is larger than that of a solid sphere or cylinder of the same mass and radius. Therefore, to achieve the same angular momentum, the hoop needs to spin at a lower angular velocity than the sphere or cylinder. But in this problem, all three objects are spinning at the same angular velocity. Since the hoop has a larger moment of inertia, it must have a larger angular momentum than the sphere or cylinder. Therefore, the correct answer is C) the hoop.

A Solid Sphere,a Solid Cylinder,and a Hoop Each Have the Same