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$

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$$}. $$What is its angular velocity after $$4\ \mathrm{s}$$?

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 in $$2.00\ \mathrm{s}$$, how many radians has it rotated through?

Accepted Answer

$$220\ \mathrm{rad}$$

Question 7

Which of the following best describes rotational kinematics?

Accepted Answer

The study of the motion of an object that rotates about an axis.

Question 8

A car tire with a radius of $$0.30\ \mathrm{m}$$ rotates at an angular velocity of $$10\ \mathrm{rad/s}. $$What is the linear speed at the edge of the tire?

Accepted Answer

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

Question 9

Which of the following is the correct relationship for the torque $$	au$$ produced by a force $$F$$ applied at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$	au = rF$$

Question 10

A solid disk of mass $$2.0\ \mathrm{kg}$$ and radius $$0.10\ \mathrm{m} is $$rotating at $$5.0\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$1.25\ \mathrm{J}$$

Question 11

Which of the following statements about points on a rotating object is correct?

Accepted Answer

Points farther from the axis move faster (greater linear speed).

Question 12

A merry-go-round accelerates from rest at $$2.0\ \mathrm{$$rad/s^2$$}$$ for $$3.0\ \mathrm{s}. $$What is its angular displacement?

Accepted Answer

$$9.0\ \mathrm{rad}$$

Question 13

Which of the following is the correct formula for the moment of inertia $$I of a $$point mass $$m at a $$distance $$r$$ from the axis?

Accepted Answer

$$I = m r^2$

Question 14

A rotating object has an angular velocity $$\omega$$ and a moment of inertia $$I. $$What is its angular momentum $$L$$?

Accepted Answer

$$L = I \omega$$

Question 15

Which of the following is the correct equation for the work $$W$$ done by a torque $$	au$$ through an angular displacement $$	heta$$?

Accepted Answer

$$W = 	au 	heta$$

Question 16

A rotating platform starts from rest and reaches an angular velocity of $$12\ \mathrm{rad/s} in$$ $$4\ \mathrm{s}. $$What is its angular acceleration?

Accepted Answer

$$3.0\ \mathrm{$$rad/s^2$$}$$

Question 17

Which of the following best defines angular acceleration?

Accepted Answer

The rate of change of angular velocity.

Question 18

A rotating object has a constant angular velocity. What is its angular acceleration?

Accepted Answer

$$0\ \mathrm{$$rad/s^2$$}$$

Question 19

Which of the following is the correct equation for the kinetic energy $$K of a $$rotating object?

Accepted Answer

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

Question 20

A child sits $$2.0\ \mathrm{m}$$ from the center of a merry-go-round spinning at $$1.5\ \mathrm{rad/s}. $$What is the child's linear speed?

Accepted Answer

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

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

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