Q: Which of the following correctly expresses Newton's Second Law for rotational motion?

$$\vec{\tau}_{\text{net}} = I_{\text{tot}} \vec{\alpha}$$

Q: Which kinematic equation describes the angular displacement $$\theta$$ for constant angular acceleration $$\alpha$$?

$$\theta_f = \theta_i + \omega_i t + \dfrac{1}{2} \alpha t^2$

Q: A merry-go-round of mass $$20\,\text{kg}$$ and radius $$2\,\text{m} is $$spun by a force $$F = 0.8\,\text{N}$$ applied tangentially at its edge. What is the angular acceleration?

$$\alpha = \dfrac{F}{I_{\text{tot}}}$$

Question 1

Which of the following correctly expresses Newton's Second Law for rotational motion?

Accepted Answer

$$\vec{	au}_{	ext{net}} = I_{	ext{tot}} \vec{\alpha}$$

Question 2

A force $$F is $$applied tangentially to the rim of a bicycle wheel of mass $$M$$ and radius $$R. $$What is the angular acceleration $$\alpha of $$the wheel?

Accepted Answer

$$\alpha = \dfrac{F}{MR^2$}$$

Question 3

Which kinematic equation describes the angular displacement $$	heta$$ for constant angular acceleration $$\alpha$$?

Accepted Answer

$$	heta_f = 	heta_i + \omega_i t + \dfrac{1}{2} \alpha t^2$

Question 4

A solid sphere and a ring have the same mass and radius. Which has the greater moment of inertia and why?

Accepted Answer

The ring, because its mass is distributed farther from the axis.

Question 5

A merry-go-round of mass $$20\,	ext{kg}$$ and radius $$2\,	ext{m} is $$spun by a force $$F = 0.8\,	ext{N}$$ applied tangentially at its edge. What is the angular acceleration?

Accepted Answer

$$\alpha = \dfrac{F}{I_{	ext{tot}}}$$

Question 6

Which equation gives the angular momentum $$L of a $$point mass $$m$$ moving with velocity $$v at a $$distance $$r$$ from the axis?

Accepted Answer

$$L = mvr \sin \beta$$

Question 7

A disk of mass $$M$$ and radius $$R$$ spins about its axis with angular velocity $$\omega. $$What is its angular momentum?

Accepted Answer

$$L = \dfrac{1}{2}MR^2$ \omega$$

Question 8

If the net external torque on a system is zero, what happens to the system's angular momentum?

Accepted Answer

It is conserved.

Question 9

A figure skater pulls in her arms while spinning. What happens to her angular velocity and why?

Accepted Answer

Her angular velocity increases because her moment of inertia decreases.

Question 10

A bullet of mass $$m$$ hits and embeds in a stationary disk of mass $$M$$ and radius $$R at $$its edge. If the system rotates after collision, which principle allows you to find the final angular velocity?

Accepted Answer

Conservation of angular momentum

Question 11

A child walks from the edge to the center of a spinning carousel. What happens to the carousel's angular velocity?

Accepted Answer

It increases because the moment of inertia decreases.

Question 12

Which of the following is the correct formula for the moment of inertia of a ring of mass $$M$$ and radius $$R$$ about its center?

Accepted Answer

$$I = MR^2$

Question 13

A rod of length $$L$$ and mass $$M is $$pivoted at its center. What is its moment of inertia about the pivot?

Accepted Answer

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

Question 14

Which statement about torque is correct?

Accepted Answer

Torque is the rotational analog of force.

Question 15

If a system's total angular momentum is conserved, which of the following must be true?

Accepted Answer

The net external torque on the system is zero.

Question 16

A rotating bat has angular momentum $$L_p$$ about a pivot axis. Which formula correctly relates $$L_p to $$the moment of inertia and angular velocity?

Accepted Answer

$$L_p = I_p \omega$$

Question 17

A person sitting on a frictionless rotating chair holds a spinning wheel. If the person flips the wheel upside down, what happens to the chair?

Accepted Answer

The chair starts spinning in the opposite direction to conserve angular momentum.

Question 18

Which of the following is the correct analogy between linear and angular momentum conservation?

Accepted Answer

$$\vec{F}_{	ext{net}} = 0 \implies \vec{p}_{	ext{total, i}} = \vec{p}_{	ext{total, f}}$$ and $$\vec{	au}_{	ext{net}} = 0 \implies \vec{L}_{	ext{total, i}} = \vec{L}_{	ext{total, f}}$$

Question 19

A planet orbits the Sun in an elliptical path. At which point is its speed greatest?

Accepted Answer

At perihelion, the closest point to the Sun.

Newton's Law for Rotation, Kinematic Equations, and Angular Momentum Conservation

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