Question 1

A solid cylinder of mass $$M$$ and radius $$R$$ rotates about its central axis. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2}MR^2$

Question 2

Which of the following objects has the greatest moment of inertia for the same mass $$M$$ and radius $$R$$ about its central axis?

Accepted Answer

A thin cylindrical shell

Question 3

A thin rod of length $$L$$ and mass $$M$$ rotates about an axis through one end, perpendicular to its length. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{3}ML^2$

Question 4

A solid sphere and a thin spherical shell have the same mass $$M$$ and radius $$R. $$Which has the smaller moment of inertia about a diameter?

Accepted Answer

The solid sphere

Question 5

What is the moment of inertia of a thin rod of mass $$M$$ and length $$L$$ about its center?

Accepted Answer

$$I = \frac{1}{12}ML^2$

Question 6

A solid cylinder and a solid sphere have the same mass $$M$$ and radius $$R. $$Which has the smaller moment of inertia about its central axis?

Accepted Answer

The solid cylinder

Question 7

For a thin cylindrical shell of mass $$M$$ and radius $$R$$, what is the moment of inertia about its central axis?

Accepted Answer

$$I = MR^2$

Question 8

A solid sphere of mass $$M$$ and radius $$R$$ rotates about a diameter. What is its moment of inertia?

Accepted Answer

$$I = \frac{2}{5}MR^2$

Question 9

A thin rod of length $$L$$ and mass $$M$$ rotates about an axis perpendicular to the rod and passing through its center. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{12}ML^2$

Question 10

Which formula gives the moment of inertia for a solid cylinder of mass $$M$$, radius $$R$$, and length $$L$$ about its central axis?

Accepted Answer

$$I = \frac{1}{2}MR^2$

Question 11

A thin spherical shell of mass $$M$$ and radius $$R$$ rotates about a diameter. What is its moment of inertia?

Accepted Answer

$$I = \frac{2}{3}MR^2$

Question 12

If you double the radius of a solid cylinder (keeping mass constant), how does its moment of inertia about its central axis change?

Accepted Answer

It increases by a factor of 4

Question 13

Which of the following objects has the smallest moment of inertia for the same mass $$M$$ and radius $$R$$ about its central axis?

Accepted Answer

Solid sphere

Question 14

A solid cylinder and a thin cylindrical shell have the same mass $$M$$ and radius $$R. $$Which has the greater moment of inertia about its central axis?

Accepted Answer

Thin cylindrical shell

Question 15

A thin rod of length $$L$$ and mass $$M$$ rotates about an axis through one end, perpendicular to its length. If the length is doubled, how does the moment of inertia change?

Accepted Answer

It increases by a factor of 4

Rotational Dynamics: Torque, Rotational Inertia, and Angular Momentum

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