1.
A child of mass m = 40 kg is playing on a merry-go-round, which has mass M = 200 kg and radius R = 2.0 m, and is initially at rest.
The child jumps off in the direction shown in the diagram, with a speed v = 5.0 m/s relative to the ground.
(a) Identify a system for which the net external torque is zero – justify your answer.
(b) What is the initial angular momentum of that system?
(c) Derive an expression for the angular velocity

of the merry-go-round after the child jumps off.
Annotate your derivation with an explanation of your approach.

(d) Determine the value of

, and discuss its reasonability by converting to rotations per second or per minute.

2.
A child of mass m = 40 kg is playing on a merry-go-round, which has mass
M = 200 kg and radius R = 2.0 m, and is initially rotating at an angular speed

0
, making one counterclockwise rotation every 3.0 seconds. The child jumps off in the direction shown in the diagram, with a speed v = 5.0 m/s relative to the merry-go-round.
(a) Identify a system for which the net external torque is zero – justify your answer.
(b) What is the initial angular momentum of that system?
(c) Explain whether the rotational speed of the merry-go-round will increase or decrease after the child jumps.

(d) Calculate the angular velocity

of the merry-go-round after the child jumps off. Annotate your calculation with an explanation of your approach.
(e) Discuss the reasonability of

by comparing to

0
and to the rotational speed in problem 1.

The above figures are not drawn to scale
3.
Four children, each of mass m = 40 kg, are riding a merry-go-round, which has mass M = 200 kg and radius R = 2.0 m. In arrangement 1, the device is spinning at an angular speed

0
, making one rotation every 3.0 seconds. The children move to arrangement 2, in which each child’s center of mass is located a distance R/2 from the merry-go-round’s center.
(a) Identify a system for which the net external torque is zero – justify your answer.
(b) What is the initial angular momentum of that system?
(c) Explain whether the rotational speed of the merry-go-round will increase or decrease after the children move to arrangement 2.

(d) Derive an expression for the angular velocity

of the merry-go-round after the children move to arrangement 2. Annotate your derivation with an explanation of your approach.
(e) Determine the value of

, and discuss its reasonability by comparing to

0
and to the rotational speed in problem 1.

4.
Four children, each of mass m = 40 kg, are riding a merry-go-round, which has mass M = 200 kg and radius R = 2.0 m. The device is spinning at an angular speed

0
, making one rotation every 3.0 seconds. The child on the left jumps off in the direction indicated, with a speed of 5.0 m/s relative to the merry-go-round.
(a) Does the angular speed of the merry-go-round increase, decrease, or remain the same after the child jumps? Justify your answer in a clear, coherent, paragraph-length response.

5.
In the video linked below (screenshot pictured), the two gray objects are dropped onto the already rotating wooden disk. Determine the mass of each gray object. Justify your answer, including both annotated calculations as well as an explanation of how you obtained the necessary data from the video. http://d32ogoqmya1dw8.cloudfront.net/files/student_videos/slab_disk_video_853.v2.mov