The inelastic collision between a disk and a rotating platform

  • Thread starter Leo Liu
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  • #1
Leo Liu
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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.
1588882549551.png

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.
 

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Answers and Replies

  • #2
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?
 
  • #3
Leo Liu
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146
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?
 
  • #4
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!
 

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