Question 1

Which of the following best explains why the North Star changes over thousands of years?

Accepted Answer

The Earth's axis of rotation precesses, causing the position of the celestial pole to shift over time.

Question 2

A wrench is used to loosen a bolt. Three equal-magnitude forces are applied: one close to the axis, one far from the axis, and one directed toward the axis. Which force is most effective at loosening the bolt and why?

Accepted Answer

The force applied farthest from the axis, because torque is maximized when the lever arm is largest.

Question 3

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

Accepted Answer

$$	au = r F \sin 	heta$$

Question 4

A child pushes tangentially on a merry-go-round of radius $$R$$ with a force $$F_{tan}. $$What is the power delivered to the merry-go-round if it rotates with angular velocity $$\omega$$?

Accepted Answer

$$P = 	au \omega$$

Question 5

Which statement about rolling without slipping is correct?

Accepted Answer

The velocity of the center of mass is equal to the angular velocity times the radius: $$v_{cm} = R \omega$$

Question 6

A solid sphere and a hollow cylinder of equal mass and radius are released from rest at the top of an incline. Which reaches the bottom first and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia and thus accelerates faster.

Question 7

What is the rotational analog of Newton's second law for a rigid body?

Accepted Answer

$$\sum 	au_z = I \alpha_z$$

Question 8

A yo-yo of mass $$M$$ and radius $$R is $$released from rest and descends a height $$h. $$What is the speed of its center of mass at the bottom, assuming no slipping?

Accepted Answer

$$v_{cm} = \sqrt{\frac{2gh}{1 + \frac{I}{MR^2$}}}$$

Question 9

The kinetic energy of a rigid body rotating and translating is given by which equation?

Accepted Answer

$$K = \frac{1}{2} M v_{cm}^2 + \frac{1}{2} I_{cm} \$$omega^2$$

Question 10

A bullet of mass $$m$$ and velocity $$v_{bullet}$$ embeds itself in a door of mass $$M$$ and length $$d$$, pivoted at one end. What is the angular velocity $$\omega of $$the door immediately after the collision?

Accepted Answer

$$\omega = \frac{m v_{bullet} \ell}{I_{total}}$$

Question 11

Which of the following best describes the conservation of angular momentum?

Accepted Answer

If the net external torque on a system is zero, the total angular momentum remains constant.

Question 12

A professor spins on a frictionless stool holding dumbbells. When the professor pulls the dumbbells inward, what happens to the angular velocity and why?

Accepted Answer

Angular velocity increases because the moment of inertia decreases and angular momentum is conserved.

Question 13

Which equation gives the angular momentum $$L of a $$rigid body rotating about a symmetry axis?

Accepted Answer

$$L = I \omega$$

Question 14

A gyroscope is spinning with angular velocity $$\omega$$ and experiences a torque $$	au$$ due to gravity. What is the direction of precession?

Accepted Answer

Perpendicular to both the angular momentum and the applied torque, following the right-hand rule.

Question 15

During a rotational collision between two disks with moments of inertia $$I_A$$ and $$I_B$$, what is conserved if no external torque acts?

Accepted Answer

Total angular momentum: $$L_{initial} = L_{final}$$

Question 16

A flywheel spins with constant angular momentum but its direction changes continuously. What physical phenomenon does this describe?

Accepted Answer

Precession

Question 17

Which of the following is the correct vector expression for torque $$\vec{	au}$$?

Accepted Answer

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

Question 18

A sphere of mass $$M$$ and radius $$R$$ rolls down an incline without slipping. What is the acceleration of its center of mass?

Accepted Answer

$$a_{cm} = \frac{g \sin \beta}{1 + \frac{I}{M R^2$}}$$

Question 19

Which of the following real-world scenarios best illustrates the conservation of angular momentum?

Accepted Answer

A figure skater spinning faster when pulling arms inward during a spin.

Dynamics of Rotational Motion: Chapter 10 Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards