3. The figure to the right shows a rod that is connected to a frictionless table through a pin-labeled by A -placed through the center of it. (You are looking down on the table.) The rod has mass m and length l. Although the rod is initially at rest, it can rotate freely (without friction) about the pin. A small particle with mass m/3, and moving with an initial velocity vo vo A collides with the end of the rod. After the collision the mass stops moving, and the rod starts rotating with angular velocity w. I would strongly recommend that you draw a free body diagram for the rod in parts a and b. a. Linear momentum is not conserved for this collision. Explain in detail why. b. Angular momentum is conserved about the pivot. Explain in detail why. c. What is w? Express it in terms of vo, and l. d. Is energy conserved in the collision? Justify your answer by calculating the change in energy of the system in the collision.

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3. The figure to the right shows a rod that is connected to
a frictionless table through a pin-labeled by
A -placed through the center of it. (You are looking
down on the table.) The rod has mass m and length l.
Although the rod is initially at rest, it can rotate freely
(without friction) about the pin. A small particle with
mass m/3, and moving with an initial velocity vo
vo
collides with the end of the rod. After the collision the
mass stops moving, and the rod starts rotating with
angular velocity w. I would strongly recommend that
you draw a free body diagram for the rod in parts a and
b.
a. Linear momentum is not conserved for this
collision. Explain in detail why.
b. Angular momentum is conserved about the pivot. Explain in detail why.
c. What is w? Express it in terms of vo, and l.
d. Is energy conserved in the collision? Justify your answer by
calculating the change in energy of the system in the collision.
e. After a time T after the collision the rod will rotate around and collide with the
small mass a second time. What is T? Express it in terms of v0, and l.
Transcribed Image Text:3. The figure to the right shows a rod that is connected to a frictionless table through a pin-labeled by A -placed through the center of it. (You are looking down on the table.) The rod has mass m and length l. Although the rod is initially at rest, it can rotate freely (without friction) about the pin. A small particle with mass m/3, and moving with an initial velocity vo vo collides with the end of the rod. After the collision the mass stops moving, and the rod starts rotating with angular velocity w. I would strongly recommend that you draw a free body diagram for the rod in parts a and b. a. Linear momentum is not conserved for this collision. Explain in detail why. b. Angular momentum is conserved about the pivot. Explain in detail why. c. What is w? Express it in terms of vo, and l. d. Is energy conserved in the collision? Justify your answer by calculating the change in energy of the system in the collision. e. After a time T after the collision the rod will rotate around and collide with the small mass a second time. What is T? Express it in terms of v0, and l.
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