1. AP Physics 1 Review Chs 8&9 Rotational Kinematics and Dynamics
Be able to perform calculations with the rotational kinematics equations and understand the relationship between rotational and translational quantities
Understand the factors that affect torque and be able to calculate torque (𝜏= 𝑟  𝐹)
Understand the concept of center of gravity and know that the torque produced by an object’s weight acts from the center of gravity
Be able to solve static equilibrium problems such as a balanced meter stick with hanging masses, ladder leaning against wall, beams supported by cables, etc.
Understand translational and rotational equilibrium and be able to identify each
Understand the concept of moment of inertia
Understand that a net torque is required for angular acceleration and be able to use 𝜏=𝐼𝛼 in calculations
Understand rotational kinetic energy and be able to use 𝐾 𝑅 = 1 2 𝐼 𝜔 2 in calculations
Be able to calculate changes in mechanical energy for an object rolling without slipping up or down an incline; understand what would happen if the incline were frictionless
Understand conservation of angular momentum and be able to use 𝐼 0 𝜔 0 = 𝐼 f 𝜔 f in calculations
Understand what happens with angular momentum, angular speed, moment of inertia, and rotational kinetic energy as a skater moves her arms inward or outward

2. Bonnie and Klyde I
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every 2 seconds.
Klyde’s angular velocity is:
a) same as Bonnie’s
b) twice Bonnie’s
c) half of Bonnie’s
d) one-quarter of Bonnie’s
e) four times Bonnie’s w
Bonnie
Klyde
Answer: a

3. Bonnie and Klyde I
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every 2 seconds.
Klyde’s angular velocity is:
a) same as Bonnie’s
b) twice Bonnie’s
c) half of Bonnie’s
d) one-quarter of Bonnie’s
e) four times Bonnie’s
The angular velocity w of any point on a solid object rotating about a fixed axis is the same. Both Bonnie and Klyde go around one revolution (2p radians) every 2 seconds. w
Bonnie
Klyde

4. Bonnie and Klyde II
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Who has the larger linear (tangential) velocity?
a) Klyde
b) Bonnie
c) both the same
d) linear velocity is zero for both of them
Answer: b w
Bonnie
Klyde

5. Bonnie and Klyde II
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Who has the larger linear (tangential) velocity?
a) Klyde
b) Bonnie
c) both the same
d) linear velocity is zero for both of them
Their linear speeds v will be different because v = r w and Bonnie is located farther out (larger radius r) than Klyde. w
Bonnie
Klyde
Answer: b
Follow-up: Who has the larger centripetal acceleration?

6. Truck Speedometer
Suppose that the speedometer of a truck is set to read the linear speed of the truck but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck?
a) speedometer reads a higher speed than the true linear speed
b) speedometer reads a lower speed than the true linear speed
c) speedometer still reads the true linear speed
Answer: b

7. Truck Speedometer
Suppose that the speedometer of a truck is set to read the linear speed of the truck but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck?
a) speedometer reads a higher speed than the true linear speed
b) speedometer reads a lower speed than the true linear speed
c) speedometer still reads the true linear speed
The linear speed is v = wR. So when the speedometer measures the same angular speed w as before, the linear speed v is actually higher, because the tire radius is larger than before.

8. e) all are equally effective
Using a Wrench a c d b
You are using a wrench to loosen a rusty nut. Which arrangement will be the most effective in loosening the nut?
Answer: b
e) all are equally effective

9. e) all are equally effective
Using a Wrench a c d b
You are using a wrench to loosen a rusty nut. Which arrangement will be the most effective in loosening the nut?
Because the forces are all the same, the only difference is the lever arm. The arrangement with the largest lever arm (case #2) will provide the largest torque.
e) all are equally effective
Follow-up: What is the difference between arrangement 1 and 4?

10. Two Forces
Two forces produce the same torque. Does it follow that they have the same magnitude?
a) yes
b) no
c) depends
Answer: b

11. Two Forces
Two forces produce the same torque. Does it follow that they have the same magnitude?
a) yes
b) no
c) depends
Because torque is the product of force times distance, two different forces that act at different distances could still give the same torque.
Follow-up: If two torques are identical, does that mean their forces are identical as well?

12. Closing a Door
In which of the cases shown below is the torque provided by the applied force about the rotation axis biggest? For all cases the magnitude of the applied force is the same.
a) F1
b) F3
c) F4
d) all of them
e) none of them
Answer: a

13. Closing a Door
In which of the cases shown below is the torque provided by the applied force about the rotation axis biggest? For all cases the magnitude of the applied force is the same.
a) F1
b) F3
c) F4
d) all of them
e) none of them
The torque is t = rFsin, and so the force that is at 90° to the lever arm is the one that will have the largest torque. Clearly, to close the door, you want to push perpendicularly!!

14. Cassette Player
When a tape is played on a cassette deck, there is a tension in the tape that applies a torque to the supply reel. Assuming the tension remains constant during playback, how does this applied torque vary as the supply reel becomes empty?
a) torque increases
b) torque decreases
c) torque remains constant
Answer: b

15. Cassette Player
When a tape is played on a cassette deck, there is a tension in the tape that applies a torque to the supply reel. Assuming the tension remains constant during playback, how does this applied torque vary as the supply reel becomes empty?
a) torque increases
b) torque decreases
c) torque remains constant
As the supply reel empties, the lever arm decreases because the radius of the reel (with tape on it) is decreasing. Thus, as the playback continues, the applied torque diminishes.

16. Moment of Inertia
Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold. Which one has the bigger moment of inertia about an axis through its center?
a) solid aluminum
b) hollow gold
c) same
same mass & radius
solid
hollow
Answer: b

17. Moment of Inertia
Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold. Which one has the bigger moment of inertia about an axis through its center?
a) solid aluminum
b) hollow gold
c) same
same mass & radius
solid
hollow
Moment of inertia depends on mass and distance from axis squared. It is bigger for the shell because its mass is located farther from the center.

18. Figure Skater a) the same b) larger because she’s rotating faster
A figure skater spins with her arms extended. When she pulls in her arms, she reduces her rotational inertia and spins faster so that her angular momentum is conserved. Compared to her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms must be
a) the same
b) larger because she’s rotating faster
c) smaller because her rotational inertia is smaller
Answer: b

19. Figure Skater a) the same b) larger because she’s rotating faster
A figure skater spins with her arms extended. When she pulls in her arms, she reduces her rotational inertia and spins faster so that her angular momentum is conserved. Compared to her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms must be:
a) the same
b) larger because she’s rotating faster
c) smaller because her rotational inertia is smaller
KErot = I 2 = L  (used L = I ). Because L is conserved, larger  means larger KErot. The “extra” energy comes from the work she does on her arms.

20. Two Disks
Two different spinning disks have the same angular momentum, but disk 1 has more kinetic energy than disk 2. Which one has the bigger moment of inertia?
a) disk 1
b) disk 2
c) not enough info L L
Answer: b
Disk 1
Disk 2

21. / Two Disks a) disk 1 b) disk 2 c) not enough info
Two different spinning disks have the same angular momentum, but disk 1 has more kinetic energy than disk 2. Which one has the bigger moment of inertia?
a) disk 1
b) disk 2
c) not enough info L L
KE = I 2 = L2 (2 I)
(used L = I ).
Because L is the same, bigger I means smaller KE. /
Disk 1
Disk 2

22. Balancing Rod 1m 1kg a) ¼ kg
b) ½ kg
c) 1 kg
d) 2 kg
e) 4 kg
A 1-kg ball is hung at the end of a rod 1-m long. If the system balances at a point on the rod 0.25 m from the end holding the mass, what is the mass of the rod?
1kg 1m
Answer: c

23. Balancing Rod
a) ¼ kg
b) ½ kg
c) 1 kg
d) 2 kg
e) 4 kg
A 1-kg ball is hung at the end of a rod 1-m long. If the system balances at a point on the rod 0.25 m from the end holding the mass, what is the mass of the rod?
The total torque about the pivot must be zero !! The CM of the rod is at its center, 0.25 m to the right of the pivot. Because this must balance the ball, which is the same distance to the left of the pivot, the masses must be the same !!
1 kg X
CM of rod
same distance
mROD = 1 kg

24. Tipping Over I
a) all
b) 1 only
c) 2 only
d) 3 only
e) 2 and 3
A box is placed on a ramp in the configurations shown below. Friction prevents it from sliding. The center of mass of the box is indicated by a red dot in each case. In which case(s) does the box tip over? 1 2 3
Answer: d

25. Tipping Over I
a) all
b) 1 only
c) 2 only
d) 3 only
e) 2 and 3
A box is placed on a ramp in the configurations shown below. Friction prevents it from sliding. The center of mass of the box is indicated by a red dot in each case. In which case(s) does the box tip over?
The torque due to gravity acts like all the mass of an object is concentrated at the CM. Consider the bottom right corner of the box to be a pivot point. 1 2 3

26. Tipping Over II
Consider the two configurations of books shown below. Which of the following is true?
a) case 1 will tip
b) case 2 will tip
c) both will tip
d) neither will tip
1/2
1/4 1 2
Answer: a

27. Tipping Over II
Consider the two configurations of books shown below. Which of the following is true?
a) case 1 will tip
b) case 2 will tip
c) both will tip
d) neither will tip
The CM of the system is midway between the CM of each book. Therefore, the CM of case #1 is not over the table, so it will tip.
1/2
1/4 1 2