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
2. 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) 10 rad/s
(E) 2 rad/s2
3. 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.
4. 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
5.
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.
6. 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
7. 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.
8. 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
9. 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.
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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
16. If the object starts from rest and accelerates with a constant angular acceleration of 6 rad/s what is
the angular 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
17. 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.
18. 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
19. 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
20. 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.
21. 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
22. 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
23. 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
24. 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
25. 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
26. Find the centripetal acceleration of the tire at t=2s.
(A) 121 m/s2 (B) 242 m/s2
(C) 308 m/s2
(E) 428 m/s2
(D) 347 m/s2
27. 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
28. 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
29. 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
30. 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