Question

Potter's Wheel Game

A scupltor is playing absent-mindedly with a large cylindrical lump of clay on a potter's wheel. This particular wheel has wonderful balance and will turn without friction when taken out of gear. The lump of clay is a uniform cylinder of mass 33.0 kg and radius 17.0 cm ; the axis of the clay cylinder coincides with the axis of the wheel, and the rotational inertia of the wheel can be neglected in comparison with the rotational inertia of the clay cylinder. The artist decides to throw ball bearings of mass 133.0 grams at the curved side wall of the turning cylinder and to watch what happens when the bearings hit and stick.

Before the first throw, the cylinder is turning once every 2.10 seconds ; when looked at from above, the cylinder is turning counterclockwise, so that the direction of the angular momentum of the cylinder is Up. The artist throws the first ball bearing horizontally, and it impacts the clay wall at an angle of 62.0 degrees away from the normal to the curved clay surface. Once the ball bearing is stuck in the clay, the cylinder is found to be turning once every 3.30 seconds , still turning counterclockwise. Consider the ball bearing to be traveling horizontally before impact; the ball bearing is traveling in a plane which is perpendicular to the axis of the clay cylinder and which contains the center of mass of the clay.

Part A

What was the angular momentum of the ball bearing, about the center of the clay cylinder, before the impact into the wall of the cylinder?

Give the Up-Down component of angular momentum, with Up being positive.

kg⋅m2/s

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Part B

What was the speed of the bearing before the collision?

m/s

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Answer 1