Q: If the minute hand of a clock completes one revolution in $$60$$ minutes, what is its angular velocity in rad/s?

$$1.75 \times 10$$^{-3}$$ $$\text{rad/s}$$

Q: A movie lasts $$2$$ hours. What is the angular displacement of the hour hand during this time?

$$\frac{2}{12} \times 2\pi = \frac{\pi}{3}$$ rad

Question 1

A DVD is rotated counterclockwise and makes one complete revolution. What is its angular displacement in radians?

Accepted Answer

$$2\pi$$

Question 2

A point on the edge of a wheel with radius $$r$$ rotates through an angle $$	heta (in $$radians). What is the formula for the linear distance $$x$$ that the point travels?

Accepted Answer

$$x = r 	heta$$

Question 3

Earth completes one revolution in 24 hours. What is Earth's angular velocity in rad/s?

Accepted Answer

$$7.27 	imes 10$$^{-5}$$

Question 4

If a car wheel accelerates from $$0.0$$ rad/s to $$78$$ rad/s in $$15 s$$, what is its average angular acceleration?

Accepted Answer

$$5.2$$ rad/s$$^2$$

Question 5

A hard drive spins at $$7200$$ RPM. What is its angular velocity in rad/s?

Accepted Answer

$$753$$ $$	ext{rad/s}$$

Question 6

A rotating toy completes one counterclockwise rotation every minute. What is its angular velocity in rad/min?

Accepted Answer

$$2\pi$$ $$	ext{rad/min}$$

Question 7

A truck has a linear acceleration of $$1.85 m/s$^2$$ and its wheels have an angular acceleration of $$5.23$$ rad/s$$^2. $$What is the diameter of the wheels?

Accepted Answer

$$0.71 m$$

Question 8

If the angular velocity of a disk is $$\omega$$ and the radius is $$r$$, what is the formula for the linear velocity $$v of a $$point on the edge?

Accepted Answer

$$v = r \omega$$

Question 9

A clothes washer drum turns at $$635$$ rev/min and slows to a stop in $$8.0 s $$after the motor is turned off. What is the angular acceleration?

Accepted Answer

$$-8.33$$ rad/s$$^2$$

Question 10

A CD-ROM has a spiral track starting at $$2.7 cm $$from the center and ending at $$5.5 cm. If $$the linear velocity of the track is kept constant at $$1.4 m/s$$, what is the angular velocity at the start of the track?

Accepted Answer

$$51.9$$ rad/s

Question 11

If the minute hand of a clock completes one revolution in $$60$$ minutes, what is its angular velocity in rad/s?

Accepted Answer

$$1.75 	imes 10$$^{-3}$$ $$	ext{rad/s}$$

Question 12

A rock sits on the Moon's equator ($$r = 1.74 	imes 10^6$ m), which rotates once every 27.3$ days. What is the linear speed of the rock due to the Moon's rotation?

Accepted Answer

$$4.63 	imes 10$$^{-2}$$ m/s

Question 13

If you replace the tires on your car with tires of larger diameter, how will the angular velocity and number of revolutions change for trips at the same speed and over the same distance?

Accepted Answer

Angular velocity decreases, number of revolutions decreases

Question 14

A movie lasts $$2$$ hours. What is the angular displacement of the hour hand during this time?

Accepted Answer

$$\frac{2}{12} 	imes 2\pi = \frac{\pi}{3}$$ rad

Question 15

Which statement best describes the angular displacement and linear distance of different points on the minute hand of a clock?

Accepted Answer

All points have the same angular displacement, but different linear distances

Question 16

A rigid body rotates at a constant angular velocity. Which statement is true about the angular velocity of points at different distances from the axis?

Accepted Answer

All points have the same angular velocity

Question 17

If a rotating object slows down, what is the sign of its angular acceleration?

Accepted Answer

Negative

Question 18

A disk's angular velocity changes from $$10$$ rad/s to $$2$$ rad/s in $$4 s. $$What is its average angular acceleration?

Accepted Answer

$$-2$$ rad/s$$^2$$

Question 19

A computer hard drive rotates at $$5400$$ RPM. What is its angular frequency in revolutions per second?

Accepted Answer

$$90$$ 	ext{rev/s}

Describing Rotational Motion: Angular Displacement, Velocity, and Acceleration

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