AP Physics C

Rotational Kinematics

Multiple Choice Questions

Problems 1-3

A disc rotates about an axis through its center according to the relation

θ (t) = t4/4 – 2t

  1. Determine the angular velocity of the disc at t= 2 s

(A)2 rad/s (B) 4 rad/s (C) 6 rad/s (D) 8 rad/s (E) 10 rad/s

  1. Determine the angular acceleration of the disc at t = 3 s.

(A)9 rad/s2 (B) 27 rad/s2 (C) 6 rad/s (D) 25 rad/s2 (E) 2 rad/s2

  1. Determine the linear speed of a point on the disc 50 cm from the center at t = 1 s.

(A)-0.5 m/s (B) -1 m/s (C)1 m/s (D) 1.5 m/s (E) 4 m/s

Problems 4-5

A hula-hoop with moment of inertia is rotating with an angular velocity of ω (t) = 3t2 – 1.

  1. Through what angular displacement will the hula-hoop move in the first 5 s?

(A)30 rad (B) 45 rad (C) 90 rad (D) 100 rad (E) 120 rad

  1. What is the linear acceleration of the hula-hoop a t= 3 s at a point of R = 2 m?

(A)3 m/s2 (B) 10 m/s2 (C) 18 m/s2 (D) 36 m/s2 (E) 48 m/s2

Problems 6-7

A rod is pivoted about its center and rotating at 2 rad/s. It increases uniformly in angular velocity to 14 rad/s in 3 s.

  1. Find the angular acceleration over the 3 s period.

(A)2 rad/s2 (B) 4 rad/s2 (C)6 rad/s2 (D)8 rad/s2 (E) 14 rad/s2

  1. Find the angular displacement over the 3 s period.

(A)24 rad (B) 48 rad (C) 3 rad (D) 2 rad (E) 12 rad

Problems 8-9

A bicycle wheel with a radius of 40 cm at a certain instant is spinning at an angular speed of 10 rad/s. The angular speed is increasing at 80 rad/s2.

  1. At this instant, find the tangential component of the bicycle’s acceleration.

(A) 8 m/s2 (B) 2 m/s2 (C) 32 m/s2 (D) 25 m/s2 (E) 40 m/s2

  1. At this instant, find the centripetal component of the bicycle’s acceleration.

(A) 12 m/s2 (B) 24 m/s2 (C) 32 m/s2 (D) 36 m/s2 (E) 40 m/s2

Problems 10-12

A record on a turntable is spinning and coming to rest. At t=0s the angular velocity of the disc is 20 rad/s and its angular acceleration is constant at -5 rad/s2.

  1. How long does it take for the record to come to rest?

(A) 2 s (B) 4 s (C) 8 s (D) 10 s (E) 12 s

  1. What is the disc’s angular velocity at t = 0.5 s?

(A) 10 rad/s (B) 15 rad/s (C) 16.5 rad/s (D)17.5 rad/s (E) 19.5 rad/s

  1. What is the angular displacement of the record through t = 2s?

(A) 30 rad (B) 15 rad (C) 40 rad (D) 50 rad (E) 25 rad

  1. A tire is rolling with an initial angular velocity of 10 rad/s. It decelerates with an angular

acceleration of 5 rad/s2 and comes to rest. What is the net angular displacement of the wheel?

(A)5 rad (B) 10 rad (C) 20 rad (D) 25 rad (E) 30 rad

  1. Find the displacement of a wheel if the radius is 8 m and the angular displacement of the wheel is 3 rad.

(A) 3 m (B) 9 m (C) 24 m (D) 36 m (E) 48 m

  1. An angular acceleration of a bowling ball is given by α (t) = 2t + 3. If the object starts from rest what is the angular velocity of the bowling ball at t = 4 s?

(A) 12 rad/s (B) 8 rad/s (C) 16 rad/s (D) 28 rad/s (E) 32 rad/s

  1. If the object starts from rest and accelerates with a constant angular acceleration of 6 rad/s what is theangular velocity at 3 s?

(A) 9.5 rad/s (B) 18 rad/s (C) 13 rad/s (D) 27 rad/s (E) 10.5 rad/s

  1. An angular acceleration of an object is given by α (t) = 3t + 2. If the object starts from rest what is the angular displacement of the object at the end of t=3s?

(A) 9.5rad (B) 22.5 rad (C) 27 rad (D) 12 rad (E) 5 rad

Problems 18-20

An object has an initial angular velocity of zero and begins to accelerate. Its new angular velocity is given by the equation, ω=4t2-5t.

  1. What is the angular velocity of the object at t=4s

(A) 44 rad/s (B) 64 rad/s (C) 84 rad/s (D) 92 rad/s (E) 104 rad/s

  1. What is the angular acceleration of the object at time t=3s?

(A) 5 rad/s2 (B) 11 rad/s2 (C) 19 rad/s2 (D) 24 rad/s2 (E) 29 rad/s2

  1. What is the angular displacement that the object covered in time t=3s

(A) 6.25 rad (B) 13.5 rad (C) 17 rad (D) 22 rad (E) 27.5 rad

Problems 21-26

A car whose tire has a radius of .5m has an angular velocity given by 3t2-5t+20.

  1. Find the angular velocity of the tire at t=2s.

(A) 14 rad/s (B) 22 rad/s (C) 24 rad/s (D) 27 rad/s (E) 30 rad/s

  1. Find the velocity of the wheel at time t=2s.

(A) 7 m/s (B) 11 m/s (C) 12 m/s (D) 13.5 m/s (E) 15 m/s

  1. What angular distance does the tire sweep through in 4 seconds?

(A) 85 rad (B) 96 rad (C) 104 rad (D) 108 rad (E) 110 rad

  1. What is the horizontal distance that the object has traveled in 4 seconds?

(A) 26 m (B) 52 m (C) 66 m (D) 72 m (E) 83 m

  1. Find the angular acceleration of the tire at t=1 second.

(A) .25 rad/s2 (B) .5 rad/s2 (C) .75 rad/s2 (D) 1 rad/s2 (E) 1.25 rad/s2

  1. Find the centripetal acceleration of the tire at t=2s.

(A) 121 m/s2 (B) 242 m/s2 (C) 308 m/s2 (D) 347 m/s2 (E) 428 m/s2

  1. An object has an initial angular velocity of 5 rad/s and undergoes an angular acceleration of 15 rad/s2. What is the final angular velocity after 3 seconds?

(A) 25 rad/s (B) 35 rad/s (C) 50 rad/s (D) 65 rad/s (E) 80 rad/s

  1. An object has a final angular velocity of 25 rad/s and sweeps through 80 rads with an angular acceleration of 2.5 rad/s2. What is the initial angular velocity?

(A) 15 rad/s (B) 25 rad/s (C) 32 rad/s (D) 48 rad/s (E) 52 rad/s

  1. An object has an initial angular velocity of 5 rad/s and undergoes a constant angular acceleration of -.1 rad/s2. What is the net distance it sweeps through in 3 seconds?

(A) 12.25 rad (B) 14.55 rad (C) 16.25 rad (D) 19.25 rad (E) 21.5 rad

  1. A ball is attached to a string and rotates in a circle. If it takes 1 second to complete 1 revolution what is the angular speed of the ball?

(A) 3.14 rad/s (B) 6.28 rad/s (C) 9.42 rad/s (D) 12.56 rad/s (E) 15.75 rad/s

Answer Key:

1.)C

2.)B

3.)A

4.)E

5.)D

6.)B

7.)A

8.)C

9.)E

10.) B

11.) D

12.) A

13.) B

14.) C

15.) D

16.) B

17.) B

18.) A

19.) C

20.) B

21.) B

22.) B

23.) C

24.) B

25.) D

26.) B

27.) C

28.) A

29.) B

30.) B