Answer to Question #28480 in Mechanics | Relativity for Emily

Question

A device consists of eight balls each of mass 0.4 kg attached to the ends of low-mass spokes of length 1.8 m, so the radius of rotation of the balls is 0.9 m. The device is mounted in the vertical plane. The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly frictionless axle. A lump of clay with mass 0.13 kg falls and sticks to one of the balls at the location shown, when the spoke attached to that ball is at 45 degrees to the horizontal. Just before the impact the clay has a speed 8 m/s, and the wheel is rotating counterclockwise with angular speed 0.20 radians/s.

(b) Just before the impact, what is the angular momentum of the combined system of device plus clay about the center C? (As usual, x is to the right, y is up, and z is out of the screen, toward you.)
LarrowitalicC,i = ???

(c) Just after the impact, what is the angular momentum of the combined system of device plus clay about the center C?
LarrowitalicC,f =???

(d) Just after the impact, what is the angular velocity of the device?
omega vecf =