A horizontal turntable is made from a uniform solid disk and is initially rotating with angular velocity of 7.5 rad/s about a fixed vertical axis through its center. The turntable has a radius of 0.35 m and a moment of inertia of 0.15925 kg m2 about the rotation axis.
A piece of clay, initially at rest, is dropped onto the turntable and sticks to it at a distance d= 0.28 m from its center as shown in the figure. The final angular velocity of the turntable and the clay after the collision is 3.7 rad/s. Treat the piece of clay as a point particle and assume that there are no external torques acting on the system around the rotation axis.
1) Which of these quantities are conserved during the collision?
a. The total linear momentum of the clay and the turntable.
b. The total angular momentum of the clay and the turntable about the rotation axis.
c. The angular momentum of the turntable about the rotation axis.
d. The angular momentum of the clay about the rotation axis.
e. The mechanical energy of the clay and the turntable
2) What is the mass of the turntable?
3) What is the angular momentum of the turntable about the rotation axis before the clay is dropped?
4) What is the total angular momentum of the turntable and the clay about the rotation axis after the collision?
5) What is the total moment of inertia of the turntable and the clay about the rotation axis after the collision?
6) What is the mass of the clay?
7) If you wanted to slow the turntable as much as possible, you should drop the clay
a. At the outside edge of the turntable.
b. At the center of the turntable.
c. Midway between the center and outside edge.