Concept #1: Intro to Angular Collisions (Two discs)

Two disks of identical mass but different radii (r and 2 r) are spinning on frictionless bearings at the same angular speed ω0 but in opposite directions. The two disks are brought slowly together. The resulting frictional force between the surfaces eventually brings them to a common angular velocity. What is the magnitude of that final angular velocity in terms of ω0?
1. ωf = 2/3 ω0
2. ωf = 1/5 ω0
3. ωf = 1/3 ω0
4. ωf = 1/2 ω0
5. ωf = 4/5 ω0
6. ωf = 3/5 ω0
7. ωf = 3/4 ω0
8. ωf = 2/5 ω0
9. ωf = 1/4 ω0

A stationary bicycle wheel of radius R is mounted in the vertical plane on a horizontal low friction axle. Initially the wheel is not rotating. The wheel has mass M, all concentrated in the rim (spokes have negligible mass). A lump of clay with mass m falls and sticks to the outer edge of the wheel at an angle θ as shown in the figure. Just before impact the clay has a speed v. Just after impact, what is the magnitude of the angular velocity of the wheel?
1. mvcosθ / MR
2. mv / (m + M)R
3. mv / MR
4. mvcosθ / (m + M)R
5. mvsinθ / (m + M)R
6. mv / (m + M)R 2
7. Mv / mR
8. Mvsinθ / mR
9. mv / MR 2
10. mvsinθ / MR

A disc with moment of inertia I1 = 40 kg • m2 and angular velocity ω1 = 20 rad/s is dropped on to a stationary second disc along the axis of rotation. The second disc has moment of inertia I2 = 60 kg • m2. How much rotational kinetic energy is lost?
A. 3200 J
B. 11300 J
C. 8000 J
D. 15000 J
E. 4800 J

A disc with moment of inertia I1 = 40 kg • m2 and angular velocity ω1 = 20 rad/s is dropped on to a stationary second disc along the axis of rotation. The second disc has moment of inertia I2 = 60 kg • m2. What is the angular velocity of the two discs?
A. 12 rad/s
B. 8 rad/s
C. 4 rad/s
D. 20 rad/s
E. 6 rad/s

A thin uniform cylindrical turntable of radius 3 m and mass 25 kg rotates in a horizontal plane with an initial angular speed of 7.9 rad/s. The turntable bearing is frictionless. A clump of clay of mass 12 kg is dropped onto the turntable and sticks at a point 1.1 m from the point of rotation.
Find the angular speed of the clay and turntable.
A. 7.75532
B. 5.75699
C. 6.99693
D. 11.0707
E. 7.097
F. 8.15289
G. 8.35556
H. 4.96894
I. 8.6087
J. 9.56476

A sticky ball collides with and sticks to rod that is floating free in space. Consider the system of the ball and the rod, and let E be the kinetic energy of the system, p the linear momentum of the system, and L the angular momentum of the system. List which of these quantities are conserved about the point where the putty strikes the rod.1. p; E2. L3. L; E4. L; p; E5. E6. p7. L; p8. none