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 object has a moment of inertia $$I = MR^2$ when rotating about its central axis?

Accepted Answer

Thin hoop, radius $$R$$

Question 3

A hollow cylinder has inner radius $$R_1$$ and outer radius $$R_2. $$What is its moment of inertia about its central axis?

Accepted Answer

$$I = \frac{1}{2}M(R_1$^2 + R_2$^2)$$

Question 4

A uniform sphere of mass $$M$$ and radius $$R$$ rotates about its center. What is its moment of inertia?

Accepted Answer

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

Question 5

A long uniform rod of mass $$M$$ and length $$L$$ rotates about its center. What is its moment of inertia?

Accepted Answer

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

Question 6

A rectangular thin plate of mass $$M$$, width $$a$$, and height $$b$$ rotates about its center. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{12}M(a^2$ + b^2$)$$

Question 7

If a thin hoop of mass $$M$$ and radius $$R$$ rotates about its diameter, what is its moment of inertia?

Accepted Answer

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

Question 8

Which of the following objects has the largest moment of inertia for the same mass $$M$$ and radius $$R$$?

Accepted Answer

Thin hoop, radius $$R$$

Question 9

A solid cylinder and a thin hoop both have mass $$M$$ and radius $$R. $$Which will roll down an incline faster, assuming no slipping?

Accepted Answer

Solid cylinder

Question 10

A long uniform rod of mass $$M$$ and length $$L$$ rotates about one end. What is its moment of inertia?

Accepted Answer

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

Question 11

Which formula would you use to calculate the moment of inertia for a composite object made of two masses $$m_1$$ and $$m_2 at $$positions $$x_1$$ and $$x_2$$?

Accepted Answer

$$I = m_1$ x_1$^2 + m_2$ x_2$^2$$

Question 12

A uniform sphere and a solid cylinder both have mass $$M$$ and radius $$R. $$Which has a smaller moment of inertia?

Accepted Answer

Uniform sphere

Question 13

If the mass of a thin hoop is doubled but its radius remains the same, how does its moment of inertia change?

Accepted Answer

It doubles

Question 14

For a thin hoop rotating about its diameter, which equation gives its moment of inertia?

Accepted Answer

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

Question 15

A rectangular thin plate of mass $$M$$, width $$a$$, and height $$b$$ rotates about its center. If $$a = b$$, what is its moment of inertia?

Accepted Answer

$$I = \frac{1}{6}Ma^2$

Question 16

Which of the following best describes why a solid cylinder rolls down an incline faster than a thin hoop?

Accepted Answer

The solid cylinder has a smaller moment of inertia relative to its mass

Question 17

A hollow cylinder with inner radius $$R_1$$ and outer radius $$R_2$$ has mass $$M. If$$ $$R_1 = 0$, what does its moment of inertia become?

Accepted Answer

$$I = \frac{1}{2}MR_2$^2$$

Question 18

If a long uniform rod rotates about its center, which equation gives its moment of inertia?

Accepted Answer

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

Question 19

A solid cylinder and a uniform sphere both have mass $$M$$ and radius $$R. $$Which has a larger moment of inertia?

Accepted Answer

Solid cylinder

Question 20

A thin hoop of mass $$M$$ and radius $$R$$ rotates about its central axis. If its radius is doubled, how does its moment of inertia change?

Accepted Answer

It quadruples

Physics Equation Sheet and Moments of Inertia Reference

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