Q: A compact disc (CD) spins at 7200 revolutions per minute (rpm). What is its angular velocity in radians per second?

$$\omega = \frac{7200 \times 2\pi}{60}$$ rad/s

Q: A child pushes a merry-go-round, causing it to accelerate from rest. If the angular acceleration is constant, which equation gives the angular displacement $$\Delta\theta$$ after time $$t$$?

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

Q: If a rotating disk has an initial angular velocity $$\$$omega_0$$ and a constant angular acceleration $$\alpha$$, what is the angular displacement $$\theta - \$$theta_0$$ after time $$t$$?

$$\theta - \$$theta_0$$ = \$$omega_0$$ t + \frac{1}{2}\alpha t^2$

Q: A tractor wheel rotates at 60 rpm. What is its angular velocity in rad/s?

$$\omega = \frac{60 \times 2\pi}{60}$$ rad/s

Question 1

A wind turbine blade rotates counterclockwise as viewed from above. If the angular displacement $$\Delta	heta is $$measured from the positive x-axis, what is the sign of the angular velocity $$\omega$$?

Accepted Answer

Positive, because counterclockwise rotation is defined as positive.

Question 2

A gyroscope is spinning with an angular velocity $$\omega$$ and experiences a constant angular acceleration $$\alpha. $$Which equation correctly describes its angular velocity after time $$t$$?

Accepted Answer

$$\omega = \$$omega_0$$ + \alpha t$$

Question 3

A compact disc (CD) spins at 7200 revolutions per minute (rpm). What is its angular velocity in radians per second?

Accepted Answer

$$\omega = \frac{7200 	imes 2\pi}{60}$$ rad/s

Question 4

A child pushes a merry-go-round, causing it to accelerate from rest. If the angular acceleration is constant, which equation gives the angular displacement $$\Delta	heta$$ after time $$t$$?

Accepted Answer

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

Question 5

A tractor wheel starts from rest and reaches an angular velocity of 25 rpm in time $$t$$ with constant angular acceleration. What will its angular velocity be after time $$2t$$?

Accepted Answer

50 rpm

Question 6

A fan blade is slowing down while rotating in the positive direction. What are the signs of $$\omega$$ and $$\alpha$$?

Accepted Answer

$$\omega is $$positive and $$\alpha is $$negative.

Question 7

A wheel turns through an angle of 25 rad in time $$t$$ starting from rest with constant angular acceleration. Through what angle will it have turned after time $$2t$$?

Accepted Answer

100 rad

Question 8

A particle moves along a circular path of radius $$r. If $$the arc length it travels is $$s$$, what is the angular displacement $$	heta in $$radians?

Accepted Answer

$$	heta = \frac{s}{r}$$

Question 9

A wind turbine blade slows down from an angular velocity $$\$$omega_1$$ to $$\$$omega_2$$ over a time interval $$\Delta t. $$What is the average angular acceleration?

Accepted Answer

$$\alpha_{av} = \frac{\$$omega_2$$ - \$$omega_1$$}{\Delta t}$$

Question 10

A merry-go-round rotates at a constant angular velocity. A boy is at the outer edge, and a girl is near the axis of rotation. How do their angular velocities compare?

Accepted Answer

Both children have the same angular velocity.

Question 11

If a rotating disk has an initial angular velocity $$\$$omega_0$$ and a constant angular acceleration $$\alpha$$, what is the angular displacement $$	heta - \$$theta_0$$ after time $$t$$?

Accepted Answer

$$	heta - \$$theta_0$$ = \$$omega_0$$ t + \frac{1}{2}\alpha t^2$

Question 12

A rotating wheel has an angular velocity $$\omega$$ and angular acceleration $$\alpha. If$$ $$\alpha is $$negative and $$\omega is $$positive, what is happening to the wheel?

Accepted Answer

The wheel is slowing down in the positive direction.

Question 13

A tractor wheel rotates at 60 rpm. What is its angular velocity in rad/s?

Accepted Answer

$$\omega = \frac{60 	imes 2\pi}{60}$$ rad/s

Question 14

A disk starts from rest and rotates with constant angular acceleration. After time $$t$$, its angular velocity is $$\omega. $$What is its angular velocity after time $$2t$$?

Accepted Answer

$$2\omega$$

Question 15

A rotating object has an angular velocity $$\$$omega_0$$ and angular acceleration $$\alpha$$. Which equation gives its angular velocity after angular displacement $$	heta - \$$theta_0$$?

Accepted Answer

$$\$$omega^2$$ = \$$omega_0$$^2 + 2\alpha (	heta - \$$theta_0$$)$$

Question 16

A merry-go-round rotates at a constant angular velocity. If a child moves from the center to the edge, what happens to their angular velocity?

Accepted Answer

It remains the same.

Question 17

A wind turbine blade rotates through an angle of $$	heta in $$time $$t. If $$the angular velocity is constant, what is the angular velocity?

Accepted Answer

$$\omega = \frac{	heta}{t}$$

Question 18

A rotating disk slows down with a constant angular acceleration. If its initial angular velocity is $$\$$omega_0$$ and it comes to rest after time t$, what is the angular acceleration?

Accepted Answer

$$\alpha = -\frac{\$$omega_0$$}{t}$$

Question 19

A rotating wheel has an angular velocity of 10 rad/s and an angular acceleration of 2 rad/s$$^2. $$What is its angular velocity after 3 seconds?

Accepted Answer

16 rad/s

Rotational Motion: Concepts, Equations, and Applications

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