Q: A point on the rim of a spinning bicycle wheel is 0.5 m from the axis and the wheel rotates at $\omega = 4$ rad/s. What is the linear speed $v$ of the point?

$v = 2$ m/s$\times$0.5 = 2$ m/s

Q: A force of 10 N is applied at an angle of $30^\circ$ to a wrench 0.2 m long. What is the torque produced?

$\tau = 0.2 \times 10 \times \sin(30^\circ) = 1$ N$\cdot$m

Question 1

Which of the following best describes the angular position of a rotating object?

Accepted Answer

The angle, measured in radians, that a reference line on the object makes with a fixed direction

Question 2

A Ferris wheel rotates counterclockwise at a constant angular velocity. Which of the following statements is TRUE about the direction of its angular velocity?

Accepted Answer

It is positive because the rotation is counterclockwise

Question 3

The angular velocity $\omega$ of a rotating object is related to its frequency $f$ by which of the following equations?

Accepted Answer

$\omega = 2\pi f$

Question 4

A point on the rim of a spinning bicycle wheel is 0.5 m from the axis and the wheel rotates at $\omega = 4$ rad/s. What is the linear speed $v$ of the point?

Accepted Answer

$v = 2$ m/s$	imes$0.5 = 2$ m/s

Question 5

If a rotating object slows down, what can be said about the signs of its angular velocity $\omega$ and angular acceleration $\alpha$?

Accepted Answer

They have opposite signs

Question 6

Which of the following correctly expresses the relationship between tangential acceleration $a_t$ and angular acceleration $\alpha$?

Accepted Answer

$a_t = r \alpha$

Question 7

A wrench 0.3 m long is used to apply a force of 50 N perpendicular to the handle. What is the torque $	au$ produced about the bolt?

Accepted Answer

$	au = 15$ N$\cdot$m

Question 8

Which component of a force produces torque about a pivot point?

Accepted Answer

The perpendicular component to the lever arm

Question 9

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

Accepted Answer

$I = \frac{1}{3} m L^2$

Question 10

If the center of gravity (CG) of an object is directly below the pivot point, what is the gravitational torque about the pivot?

Accepted Answer

Zero

Question 11

A solid disk and a hoop, both of mass $M$ and radius $R$, roll down an incline without slipping. Which reaches the bottom first and why?

Accepted Answer

The disk, because it has a smaller moment of inertia

Question 12

Which equation represents Newton’s Second Law for rotational motion?

Accepted Answer

$	au = I \alpha$

Question 13

A child sits at the edge of a merry-go-round spinning at constant speed. If the child moves closer to the center, what happens to the angular velocity, assuming no external torque?

Accepted Answer

It increases

Question 14

Which of the following is TRUE about rolling without slipping?

Accepted Answer

The point of contact with the ground is momentarily at rest

Question 15

A force of 10 N is applied at an angle of $30^\circ$ to a wrench 0.2 m long. What is the torque produced?

Accepted Answer

$	au = 0.2 	imes 10 	imes \sin(30^\circ) = 1$ N$\cdot$m

Question 16

Which of the following statements about moment of inertia is correct?

Accepted Answer

It depends on both the mass and its distribution relative to the axis

Question 17

A seesaw is balanced when two children of different masses sit at different distances from the pivot. Which principle explains this balance?

Accepted Answer

The sum of the torques about the pivot is zero

Question 18

If a rotating object has a large moment of inertia, what can be said about its angular acceleration for a given torque?

Accepted Answer

It will be smaller

Question 19

A gymnast spins faster when pulling her arms in. Which law or principle explains this phenomenon?

Accepted Answer

Conservation of angular momentum

Question 20

Which of the following is the correct SI unit for angular acceleration?

Accepted Answer

radians per second squared

Rotational Motion: Key Concepts and Formulas

Study Guide - Practice Questions

Study Guide - Flashcards