Question

A sculptor 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 25.0 kg

and radius 19.0 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 137.0 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 58.0 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?

Part B:
What was the speed of the bearing before the collision?

Answer 1

The angular momentum of the ball bearing before the impact is 0 kg·m^2/s. The speed of the bearing before the collision is approximately 0.574 m/s.

Step-by-step explanation:

Part A: The angular momentum of the ball bearing, before the impact, can be calculated using the formula:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. Since the ball bearing is traveling horizontally before impact, its angular velocity is zero. The moment of inertia of the ball bearing can be calculated using the formula:

I = mR^2

where m is the mass of the ball bearing and R is the radius of the clay cylinder. Plugging in the values, we get:

I = (0.137 kg)(0.19 m)^2 = 0.004286 kg·m^2

Therefore, the angular momentum of the ball bearing before the impact is:

L = (0.004286 kg·m^2)(0 rad/s) = 0 kg·m^2/s

Part B: The speed of the bearing before the collision can be calculated using the formula:

v = ωR

where v is the speed, ω is the angular velocity, and R is the radius of the clay cylinder. Plugging in the values, we get:

v = (0.19 m)(2π rad/2.10 s) ≈ 0.574 m/s