Q: Which of the following statements about rolling without slipping is correct?

The velocity of the center of mass $$v_{\text{cm}}$$ equals the product of the angular velocity $$\omega$$ and the radius $$R$$: $$v_{\text{cm}} = \omega R.$$

Q: A rigid body rotates about a fixed axis with angular acceleration $$\alpha. If $$the net external torque is $$\tau_{\text{net}}$$ and the moment of inertia is $$I$$, which equation describes the rotational analog of Newton's second law?

$$\tau_{\text{net}} = I \alpha$$

Q: A drag racer’s tires are spinning and smoke is rising from them. Which statement is true about the motion of the tires?

The tires are slipping, so $$v_{\text{cm}} \neq \omega R.$$

Question 1

A mechanic uses a wrench to loosen a bolt. Which of the following actions will produce the greatest torque on the bolt?

Accepted Answer

Applying a force perpendicular to the wrench at the end farthest from the bolt.

Question 2

Which equation correctly expresses the torque $$	au$$ produced by a force $$\vec{F}$$ acting at a distance $$r$$ from the axis of rotation at an angle $$\phi$$?

Accepted Answer

$$	au = rF \sin \phi$$

Question 3

A child pushes a merry-go-round with a tangential force $$F at a $$distance $$r$$ from the center. What is the work $$W$$ done by the child after the merry-go-round rotates through an angle $$\Delta 	heta$$?

Accepted Answer

$$W = 	au \Delta 	heta$$

Question 4

Which of the following statements about rolling without slipping is correct?

Accepted Answer

The velocity of the center of mass $$v_{	ext{cm}}$$ equals the product of the angular velocity $$\omega$$ and the radius $$R$$: $$v_{	ext{cm}} = \omega R.$$

Question 5

A rigid body rotates about a fixed axis with angular acceleration $$\alpha. If $$the net external torque is $$	au_{	ext{net}}$$ and the moment of inertia is $$I$$, which equation describes the rotational analog of Newton's second law?

Accepted Answer

$$	au_{	ext{net}} = I \alpha$$

Question 6

A spinning figure skater pulls in her arms, reducing her moment of inertia from $$I_1 to$$ $$I_2. If no $$external torque acts, what happens to her angular velocity $$\omega$$?

Accepted Answer

$$\omega$$ increases so that $$I_1$$ \$$omega_1$$ = $$I_2$$ \$$omega_2$$

Question 7

Which of the following best describes the direction of the torque vector $$\vec{	au}$$ produced by a force $$\vec{F}$$ applied at position vector $$\vec{r}$$?

Accepted Answer

It is given by the right-hand rule for the cross product $$\vec{	au} = \vec{r} 	imes \vec{F}.$$

Question 8

A solid disk of mass $$M$$ and radius $$R$$ rolls without slipping down an incline. What is the total kinetic energy $$K of $$the disk when its center of mass moves at speed $$v$$?

Accepted Answer

$$K = \frac{1}{2} M v^2$ + \frac{1}{2} I \$$omega^2$$

Question 9

A gyroscope is spinning with angular momentum $$\vec{L}$$ and experiences a torque $$\vec{	au}$$ perpendicular to $$\vec{L}. $$What is the resulting motion of the gyroscope's axis?

Accepted Answer

The axis precesses around the direction of the torque.

Question 10

Which condition must be met for the conservation of angular momentum to apply to a system?

Accepted Answer

The net external torque on the system must be zero.

Question 11

A drag racer’s tires are spinning and smoke is rising from them. Which statement is true about the motion of the tires?

Accepted Answer

The tires are slipping, so $$v_{	ext{cm}} 
eq \omega R.$$

Question 12

A torque $$	au is $$applied to a rotating body for a time $$\Delta t. $$What is the change in angular momentum $$\Delta L of $$the body?

Accepted Answer

$$\Delta L = 	au \Delta t$$

Question 13

A maple seed falls while spinning. What effect does the rotation have on its descent?

Accepted Answer

It slows the descent by increasing air resistance.

Question 14

A rigid body is acted upon by two equal and opposite internal forces. What is the net torque produced by these forces about the center of mass?

Accepted Answer

Zero, because the torques cancel each other.

Question 15

A helicopter’s main rotor spins at a constant rate. What can be said about the net work done on the rotor?

Accepted Answer

The net work is zero because the positive work by the engine is balanced by the negative work of air resistance.

Question 16

Which of the following is the correct expression for the angular momentum $$L of a $$rigid body rotating about a symmetry axis?

Accepted Answer

$$L = I \omega$$

Question 17

A sphere rolls on a surface that deforms slightly. What is the main effect of this deformation?

Accepted Answer

Mechanical energy is lost, slowing the motion.

Question 18

A cat falls and twists its body to land on its feet. What principle allows the cat to do this?

Accepted Answer

Conservation of angular momentum, as the net external torque is zero.

Dynamics of Rotational Motion: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards