Problem 11.36
A rotating uniform-density disk of radius 0.7 m is mounted in the vertical plane. The axle is held up by supports that are not shown, and the disk is free to rotate on the nearly frictionless axle. The disk has mass 5.6 kg. A lump of clay with mass 0.3 kg falls and sticks to the outer edge of the wheel at location A, ⟨-0.49,0.500,0⟩ m. (Let the origin of the coordinate system be the center of the disk.) Just before the impact, the clay has a speed of 8 m/s, and the disk is rotating clockwise with an angular speed of 0.50 radians/s.
(a) Just before the impact, what is the angular momentum of the combined system of the wheel 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.)
L_c,i = ⟨, , ⟩ kg·m^2/s
(b) Just after the impact, what is the angular momentum of the combined system of the wheel plus clay about the center C?
L_c,f = ⟨, , ⟩ kg·m^2/s
(c) Just after the impact, what is the angular velocity of the wheel?
ω_f = ⟨, , ⟩ radians/s
(d) Qualitatively, what happens to the linear momentum of the combined system? (Think about why this is.)
There is no change because linear momentum is always conserved.
Some of the linear momentum is changed into energy.
Some of the linear momentum is changed into angular momentum.
The downward linear momentum decreases because the axle exerts an upward force.