Initially a platter rotates without friction about a vertica

Initially, a platter rotates without friction about a vertical axis through its center when a non-rotating platter is dropped onto it. After a brief period of sliding between them, the two platters rotate together at a lower final angular velocity. What are the signs of the change in angular momentum (L = L_f –L_i) and kinetic energy (K = K_f –K_i)?

Solution

For one platter being dropped on the other, there is no external force acting on the system, hence, the final angular velocity is achieved in such a way that the net angular momentum remains conserved. That would mean that the final angular momentum will be same as the initial angular momentum,

That is Lf - Li = Zero.

Now, as the second platter is dropped, it is accelerated by the already rotating platter by the frictional force acting on them. At the same time, the first platter is slowed down by this action. In totality, some amount of energy is lost as the result of action of friction, hence the final kinetic energy will be less than the initial kinetic energy.

That is Kf - Ki will be negative.