Q: A wheel rotates from rest with a constant angular acceleration $$\alpha. $$Which equation gives the angular displacement $$\theta$$ after time $$t$$?

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

Q: Which of the following is the correct unit for angular acceleration $$\alpha$$?

$$\text{radians per second squared}$$

Q: A rotating disk has an angular velocity $$\omega = 4\ \text{rad/s}$$ and a moment of inertia $$I = 2\ \text{kg} \cdot \text{m}^2. $$What is its angular momentum $$L$$?

$$8\ \text{kg} \cdot \text{m}^2/\text{s}$$

Q: A force of $$5\ \text{N} is $$applied perpendicular to a wrench at a distance of $$0.3\ \text{m}$$ from the pivot. What is the torque produced?

$$1.5\ \text{N} \cdot \text{m}$$

Question 1

Which of the following best describes a radian?

Accepted Answer

A unit of angular measurement defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.

Question 2

If an object moves through an angle of $$	heta = 3\pi$$ radians, how many complete revolutions has it made?

Accepted Answer

$$1.5$$ revolutions

Question 3

Given a circle of radius $$r$$, what is the formula for the arc length $$s$$ subtended by a central angle $$	heta (in $$radians)?

Accepted Answer

$$s = r 	heta$$

Question 4

A wheel rotates from rest with a constant angular acceleration $$\alpha. $$Which equation gives the angular displacement $$	heta$$ after time $$t$$?

Accepted Answer

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

Question 5

Which of the following is the correct unit for angular acceleration $$\alpha$$?

Accepted Answer

$$	ext{radians per second squared}$$

Question 6

A rotating disk has an angular velocity $$\omega = 4\ 	ext{rad/s}$$ and a moment of inertia $$I = 2\ 	ext{kg} \cdot 	ext{m}^2. $$What is its angular momentum $$L$$?

Accepted Answer

$$8\ 	ext{kg} \cdot 	ext{m}^2/	ext{s}$$

Question 7

Which of the following is the correct rotational analog of Newton's second law ($$F = ma$$)?

Accepted Answer

$$	au = I \alpha$$

Question 8

A force of $$5\ 	ext{N} is $$applied perpendicular to a wrench at a distance of $$0.3\ 	ext{m}$$ from the pivot. What is the torque produced?

Accepted Answer

$$1.5\ 	ext{N} \cdot 	ext{m}$$

Question 9

Which of the following statements about radians is TRUE?

Accepted Answer

Radians are technically unitless, but are used to indicate angular measurement.

Question 10

A car tire rotates $$720$$ degrees. How many radians has it rotated through?

Accepted Answer

$$4\pi$$ radians

Question 11

Which of the following is the correct translation between linear and angular variables?

Accepted Answer

Linear velocity $$v$$ corresponds to angular velocity $$\omega$$

Question 12

If a rotating object has an angular acceleration $$\alpha = 2\ 	ext{rad/s}^2$$ and a moment of inertia $$I = 3\ 	ext{kg} \cdot 	ext{m}^2$$, what is the net torque $$	au$$ acting on it?

Accepted Answer

$$6\ 	ext{N} \cdot 	ext{m}$$

Question 13

Which of the following is the correct formula for the rotational kinetic energy of a rigid body?

Accepted Answer

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

Question 14

A point on the rim of a rotating disk moves with a linear speed $$v. If $$the disk has radius $$r$$ and angular velocity $$\omega$$, which equation relates these quantities?

Accepted Answer

$$v = r \omega$$

Question 15

Which of the following is NOT a correct pair of linear and angular analogs?

Accepted Answer

Linear force $$F$$ and angular momentum $$L$$

Question 16

A rotating object starts from rest and accelerates at $$\alpha = 4\ 	ext{rad/s}^2$$ for $$t = 3\ 	ext{s}. $$What is its final angular velocity $$\omega$$?

Accepted Answer

$$12\ 	ext{rad/s}$$

Question 17

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

Accepted Answer

It is the rotational analog of mass and depends on the mass distribution relative to the axis of rotation.

Question 18

A spinning figure skater pulls in her arms, reducing her moment of inertia to half its original value. If no external torque acts, what happens to her angular velocity?

Accepted Answer

It doubles.

Question 19

Which of the following is the correct angular kinematic equation analogous to $$v^2 = v$$_$$i^2 + 2a(x - x_i$$)$$?

Accepted Answer

$$\$$omega^2$$ = \omega_i^2$ + 2\alpha (	heta - 	heta_i)$$

Rotational Motion and Rotational Kinematics: Translation Between Linear and Angular Variables

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