Q: A solid disk of mass $$2\,\text{kg}$$ and radius $$0.5\,\text{m}$$ rotates about its center. What is its moment of inertia?

$$0.25\,\text{kg}\cdot\text{m}^2$$

Q: Which equation correctly relates angular displacement $$\theta$$, angular velocity $$\omega$$, and angular acceleration $$\alpha$$ for constant acceleration?

$$\theta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Q: Which of the following is the correct analogy between Newton’s 2nd law for linear and rotational motion?

$$F = ma$$ \text{and} $$\tau = I\alpha$$

Q: A $$2\,\text{kg}$$ ring of radius $$0.4\,\text{m}$$ rotates at $$5\,\text{rad/s}. $$What is its angular momentum?

$$1.6\,\text{kg}\cdot\text{m}^2/\text{s}$$

Q: A $$0.2\,\text{kg}$$ mass is attached to a $$0.5\,\text{m}$$ rod and rotated about one end. What is the moment of inertia?

$$0.05\,\text{kg}\cdot\text{m}^2$$

Question 1

A wheel rotates through $$3$$ revolutions. What is the angular displacement in radians?

Accepted Answer

$$6\pi$$

Question 2

A wrench is used to loosen a bolt. If a force of $$20\,	ext{N} is $$applied at a distance of $$0.25\,	ext{m}$$ from the bolt, what is the torque produced?

Accepted Answer

$$5\,	ext{N}\cdot	ext{m}$$

Question 3

A uniform beam of mass $$10\,	ext{kg}$$ and length $$2\,	ext{m} is $$supported at its ends. A $$15\,	ext{kg}$$ mass is placed $$0.5\,	ext{m}$$ from the left end. What is the force on the right support?

Accepted Answer

$$122.5\,	ext{N}$$

Question 4

Which statement best describes the moment of inertia?

Accepted Answer

It is a measure of how mass is distributed relative to the axis of rotation.

Question 5

A solid disk of mass $$2\,	ext{kg}$$ and radius $$0.5\,	ext{m}$$ rotates about its center. What is its moment of inertia?

Accepted Answer

$$0.25\,	ext{kg}\cdot	ext{m}^2$$

Question 6

Which equation correctly relates angular displacement $$	heta$$, angular velocity $$\omega$$, and angular acceleration $$\alpha$$ for constant acceleration?

Accepted Answer

$$	heta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Question 7

A rotating object has an angular velocity of $$10\,	ext{rad/s}$$ and completes $$5$$ revolutions. What is the period of one revolution?

Accepted Answer

$$0.628\,	ext{s}$$

Question 8

A massless string is wrapped around a pulley of radius $$0.2\,	ext{m}$$ and moment of inertia $$0.5\,	ext{kg}\cdot	ext{m}^2. If a$$ $$10\,	ext{N}$$ force pulls the string, what is the angular acceleration?

Accepted Answer

$$4\,	ext{rad/s}^2$$

Question 9

Which of the following is the correct analogy between Newton’s 2nd law for linear and rotational motion?

Accepted Answer

$$F = ma$$ 	ext{and} $$	au = I\alpha$$

Question 10

A figure skater spins with arms extended and then pulls them in, reducing her moment of inertia by half. If her initial angular velocity was $$2\,	ext{rad/s}$$, what is her final angular velocity?

Accepted Answer

$$4\,	ext{rad/s}$$

Question 11

A $$1\,	ext{kg}$$ solid sphere rolls without slipping down a $$2\,	ext{m}$$ high incline. What is its speed at the bottom?

Accepted Answer

$$4.7\,	ext{m/s}$$

Question 12

Which formula gives the total kinetic energy of a rolling object?

Accepted Answer

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

Question 13

A $$0.5\,	ext{kg}$$ mass is attached to a string and swung in a circle of radius $$0.3\,	ext{m} at$$ $$2\,	ext{Hz}. $$What is the angular velocity?

Accepted Answer

$$4\pi\,	ext{rad/s}$$

Question 14

A seesaw is $$4\,	ext{m}$$ long and has a $$30\,	ext{kg}$$ child sitting $$1\,	ext{m}$$ from the left end. Where should a $$40\,	ext{kg}$$ child sit from the right end to balance the seesaw?

Accepted Answer

$$0.75\,	ext{m}$$

Question 15

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

Accepted Answer

The total angular momentum of a system remains constant if no external torque acts on it.

Question 16

A rotating merry-go-round has a moment of inertia $$I$$ and angular velocity $$\omega. If a $$child jumps onto it, increasing the moment of inertia to $$1.5I$$, what is the new angular velocity?

Accepted Answer

$$\frac{2}{3}\omega$$

Question 17

A $$2\,	ext{kg}$$ ring of radius $$0.4\,	ext{m}$$ rotates at $$5\,	ext{rad/s}. $$What is its angular momentum?

Accepted Answer

$$1.6\,	ext{kg}\cdot	ext{m}^2/	ext{s}$$

Question 18

A car tire of radius $$0.3\,	ext{m}$$ rotates at $$600\,	ext{rpm}. $$What is its angular velocity in $$	ext{rad/s}$$?

Accepted Answer

$$62.8\,	ext{rad/s}$$

Question 19

A $$0.2\,	ext{kg}$$ mass is attached to a $$0.5\,	ext{m}$$ rod and rotated about one end. What is the moment of inertia?

Accepted Answer

$$0.05\,	ext{kg}\cdot	ext{m}^2$$

Circular Motion, Rotational Mechanics, and Statics: Study Guide

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