Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Angular Collisions Two disks are initially spinning above one another on a small

ID: 1498886 • Letter: A

Question

Angular Collisions Two disks are initially spinning above one another on a small axle that provides a very tiny torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.72 m. Disk 1 has a moment of inertia I_1, = 10 kg-m^2. Disk 2 has a moment of inertia I_2 = 13.0 kg-m^2. Disk 1 is initially spinning with angular velocity omega_1 = 19.3 rad/s, and disk 2 is initially spinning with angular velocity omega_2 = -23.2 rad/s. Disk 1 is then dropped on disk 2, and eventually the two discs reach a common, final angular velocity. Find their final angular velocity. Let counteclockwise rotation as viewed from above be positive. How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small.

Explanation / Answer

Angular momentum of the system is conserved.

I11 + I22 = (I1 + I2)

=> = [(10 * 19.3) - (13 * 23.2)] / (10 + 13) = -4.72 rad/s

So the disks will be moving in clockwise direction.

Etherm = K = I112/2 + I222/2 - (I1 + I2)2

=> Etherm = (10 * 19.32 / 2) + (13 * 23.22 / 2) - [(10 + 13) * 4.722 / 2] = 5104.8 J