AP Physics C: Mechanics 6.3 Angular Momentum and Angular Impulse Questions

Mech.3.
A uniform rod of length d has one end fixed to the central axis of a horizontal, frictionless circular platform of radius R=2 d. Fixed at the other end of the rod is an ideal spring of negligible mass to which a block is attached. The block is set in frictionless grooves so that it can only move along a radius of the platform, as shown in Figure 1 above. The equilibrium length of the spring is d / 2. Below is a table showing the mass of the block and the masses and rotational inertias of the rod and platform.

A motor begins to slowly rotate the platform counterclockwise as viewed from above until the platform reaches a constant angular speed $\omega$. Under these conditions, the spring has stretched by an additional length d / 2, as shown in Figure 2.

Answer the following questions for the platform rotating at constant angular speed $\omega$. Express all algebraic answers in terms of $m, d, \omega$, and physical constants, as appropriate.

Determine an expression for the angular momentum of the entire system about the axis of the platform.

While the system continues to rotate, a small mechanism in the pivot moves the rod slowly until the center of the rod is positioned on the axis, as shown in Figure 3 above. The same constant angular speed $\omega$ is maintained by the motor driving the platform.

Questions 14-16 A ball of mass 2.0 kg is thrown vertically upward from the top of a building. The ball's velocity v is given as a function of time t by the equation v(t)=R-S t, where $R=5 \mathrm{~m} / \mathrm{s}$ and $S=10 \mathrm{~m} / \mathrm{s}^{2}$. The positive direction is upward.

18. The interval of time $\Delta t$ is the elapsed time from the moment of first contact between the two disks until they are both spinning at the same angular velocity. Which of the following expressions gives the magnitude of the average torque that the first disk exerts on the second disk?