Q: Which of the following is the correct formula for the angular displacement $$\theta$$ under constant angular acceleration?

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

Q: A disk rotates from rest with a constant angular acceleration. After $$t$$ seconds, which equation gives the angular displacement $$\theta$$?

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

Question 1

Which of the following best describes translational kinematics?

Accepted Answer

The study of the motion of an object in which all parts move the same distance in the same direction over time.

Question 2

A wheel starts from rest and undergoes a constant angular acceleration of $$\alpha = 5\ \mathrm{$$rad/s^2$$}$$ for $$t = 4\ \mathrm{s}. $$What is its final angular velocity $$\omega$$?

Accepted Answer

$$\omega = 20\ \mathrm{rad/s}$$

Question 3

Which equation correctly relates linear velocity $$v$$ and angular velocity $$\omega$$ for a point at radius $$r$$ from the axis of rotation?

Accepted Answer

$$v = r\omega$$

Question 4

A fishing reel with a radius of $$0.0450\ \mathrm{m} is $$given an angular acceleration of $$110\ \mathrm{$$rad/s^2$$}$$ from rest. What is the speed of the fishing line leaving the reel after $$2.00\ \mathrm{s}$$?

Accepted Answer

$$9.90\ \mathrm{m/s}$$

Question 5

Which of the following is the correct formula for the angular displacement $$	heta$$ under constant angular acceleration?

Accepted Answer

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

Question 6

If a rotating disk makes $$35.0$$ revolutions, how many radians has it rotated through?

Accepted Answer

$$220\ \mathrm{rad}$$

Question 7

Which of the following best defines angular acceleration?

Accepted Answer

The rate of change of angular velocity.

Question 8

A car tire rotates with a constant angular velocity. What is the linear velocity of a point on the edge of the tire if the radius is $$0.3\ \mathrm{m}$$ and the angular velocity is $$10\ \mathrm{rad/s}$$?

Accepted Answer

$$3.0\ \mathrm{m/s}$$

Question 9

Which of the following statements about rotational motion is correct?

Accepted Answer

Points farther from the axis of rotation move with greater linear speed.

Question 10

A solid disk and a hollow ring have the same mass and radius. Which has the greater rotational inertia?

Accepted Answer

The hollow ring.

Question 11

Which equation gives the relationship between torque $$	au$$, force $$F$$, and lever arm $$r$$?

Accepted Answer

$$	au = F r$$

Question 12

A rotating object starts from rest and reaches an angular velocity of $$50\ \mathrm{rad/s} in$$ $$5\ \mathrm{s}. $$What is its angular acceleration?

Accepted Answer

$$10\ \mathrm{$$rad/s^2$$}$$

Question 13

Which of the following is the correct unit for angular displacement?

Accepted Answer

$$\mathrm{rad}$$

Question 14

A point on a rotating wheel travels an arc length $$s in $$time $$t. $$Which formula relates arc length $$s$$, radius $$r$$, and angular displacement $$	heta$$?

Accepted Answer

$$s = r 	heta$$

Question 15

Which of the following best describes the difference between translational and rotational kinematics?

Accepted Answer

Translational kinematics deals with motion along a path, while rotational kinematics deals with motion about an axis.

Question 16

A rotating object has an angular velocity $$\omega = 30\ \mathrm{rad/s}$$ and a radius $$r = 0.2\ \mathrm{m}. $$What is the linear velocity $$v at $$the edge?

Accepted Answer

$$6.0\ \mathrm{m/s}$$

Question 17

Which of the following is NOT a characteristic of rotational motion?

Accepted Answer

All points move the same distance in the same direction.

Question 18

A disk rotates from rest with a constant angular acceleration. After $$t$$ seconds, which equation gives the angular displacement $$	heta$$?

Accepted Answer

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

Question 19

Which of the following is the correct formula for the rotational kinetic energy of a rotating object?

Accepted Answer

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

Question 20

A rotating object has a moment of inertia $$I = 2\ \mathrm{kg\cdot m^2$}$$ and angular velocity $$\omega = 5\ \mathrm{rad/s}. $$What is its angular momentum $$L$$?

Accepted Answer

$$L = 10\ \mathrm{kg\cdot m^2$/s}$$

Translational and Rotational Kinematics: Definitions, Key Terms, and Example Problems

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