Q: A solid sphere rolls smoothly down a ramp inclined at angle $$\theta. $$Which equation gives the acceleration of the center of mass of the sphere?

$$a_{com,x} = -\frac{g \sin \theta}{1 + \frac{I_{com}}{MR^2$}}$$

Q: Which of the following best describes the relationship between torque and angular momentum for a single particle?

$$\vec{\tau}_{net} = \frac{d\vec{\ell}}{dt}$$

Q: A particle moves in a straight line, but its position vector $$\vec{r}$$ and momentum $$\vec{p}$$ are not parallel. What is the angular momentum of the particle about the origin?

$$\vec{L} = \vec{r} \times \vec{p}$$

Question 1

A solid sphere rolls smoothly down a ramp inclined at angle $$	heta. $$Which equation gives the acceleration of the center of mass of the sphere?

Accepted Answer

$$a_{com,x} = -\frac{g \sin 	heta}{1 + \frac{I_{com}}{MR^2$}}$$

Question 2

A yo-yo of mass $$M$$ and radius $$R_0$$ descends its string. If its moment of inertia about the center of mass is $$I_{com}$$, what is the linear acceleration of its center of mass?

Accepted Answer

$$a_{com} = -\frac{g}{1 + \frac{I_{com}}{MR_0$^2}}$$

Question 3

A rolling object has two types of kinetic energy. Which equation correctly expresses the total kinetic energy for a rolling object?

Accepted Answer

$$K = \frac{1}{2}I_{com}\$$omega^2$$ + \frac{1}{2}Mv_{com}^2$$

Question 4

A disk rolls up a frictionless incline and another identical disk rolls up a rough incline. Both start with the same speed. Which disk reaches a greater height?

Accepted Answer

The disk on the frictionless incline reaches a greater height.

Question 5

The rear wheel of a bicycle has twice the radius of the front wheel. When the bicycle is moving, how does the angular speed of the rear wheel compare to that of the front wheel?

Accepted Answer

The rear wheel has less angular speed.

Question 6

Which of the following best describes the relationship between torque and angular momentum for a single particle?

Accepted Answer

$$\vec{	au}_{net} = \frac{d\vec{\ell}}{dt}$$

Question 7

A gyroscope spins rapidly and precesses about a vertical axis. Which equation gives the precession rate $$\Omega$$?

Accepted Answer

$$\Omega = \frac{Mgr}{I\omega}$$

Question 8

A disk, a hoop, and a solid sphere (all with the same mass and radius) are spun by pulling a string with the same constant tangential force. Which object has the greatest angular speed after a fixed time?

Accepted Answer

The solid sphere

Question 9

A rhinoceros beetle rides the rim of a disk rotating about its central axis. If the beetle crawls toward the center, what happens to the angular momentum of the beetle-disk system (assuming no external torque)?

Accepted Answer

It remains the same

Question 10

Which of the following statements about angular momentum is correct?

Accepted Answer

Angular momentum is a vector quantity and must be measured relative to a specified origin.

Question 11

A particle moves in a straight line, but its position vector $$\vec{r}$$ and momentum $$\vec{p}$$ are not parallel. What is the angular momentum of the particle about the origin?

Accepted Answer

$$\vec{L} = \vec{r} 	imes \vec{p}$$

Question 12

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

Accepted Answer

It remains constant.

Question 13

A student spinning on a stool pulls her arms in. What happens to her rotational inertia and angular speed, assuming angular momentum is conserved?

Accepted Answer

Rotational inertia decreases, angular speed increases.

Question 14

Which equation correctly relates the net torque on a system of particles to the rate of change of the system's total angular momentum?

Accepted Answer

$$\vec{	au}_{net} = \frac{d\vec{L}}{dt}$$

Question 15

A wheel rolls smoothly without slipping. What is the relationship between the center-of-mass speed $$v_{com}$$ and the angular speed $$\omega$$?

Accepted Answer

$$v_{com} = \omega R$$

Question 16

A force $$\vec{F}$$ acts at a distance $$\vec{r}$$ from a point O. Which equation gives the torque about O?

Accepted Answer

$$\vec{	au} = \vec{r} 	imes \vec{F}$$

Question 17

A gyroscope's precession rate is independent of which of the following quantities?

Accepted Answer

Mass $$M$$

Question 18

Which of the following is true for a smoothly rolling object on a horizontal surface?

Accepted Answer

The frictional force points in the direction of acceleration.

Question 19

A long jumper windmills her arms during flight. What is the purpose of this action in terms of angular momentum?

Accepted Answer

To transfer angular momentum and keep her upright.

Rolling, Torque, and Angular Momentum: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard