The inelastic collision between a disk and a rotating platform

[Leo Liu]

Homework Statement

A FR question in 2019 AP Physics C Exam (Version 2)

Relevant Equations

Rotational Kinetic Energy, Conservation of Angular Momentum

A disk is dropped on a platform rotating at a constant angular speed $\omega_i$ as shown below.

The question asks whether the final kinetic energy of the platform is conserved. I understand the angular momentum is always conserved provided that the net torque is 0, so I wrote the following equation:
$$I_{platform} \omega_i = (I_{platform}+I_{disk}) \omega_f$$
From this I inferred that $\frac 1 2 I_{platform} {\omega_i}^2 \neq \frac 1 2 (I_{platform}+I_{disk}) {\omega_f}^2$.

My questions are as follows: Why is the energy not conserved in the collision, and how is the energy dissipated?

Thank you in advance.

 

[etotheipi]

What force must act between the platform and the disk in order to equalise their angular velocities? Does this force dissipate mechanical energy into anything else?

 

[Leo Liu]

What force must act between the platform and the disk in order to equalise their angular velocities? Does this force dissipate mechanical energy into anything else?

I think it's kinetic friction because the angular speed of the platform decreases as the rotation of the disk speeds up. Am I right?

 

[etotheipi]

I think it's kinetic friction because the angular speed of the platform decreases as the rotation of the disk speeds up. Am I right?

Yes that's right.

And friction dissipates mechanical energy into thermal energy. Actually, the total work done by friction at the interface, $W$, is the change in mechanical energy of the system. The change in thermal energy of the system is $-W$. Energy is conserved... just not KE!