Question

What happens to the angular velocity of a circular platform when you place a block mass on it? (in terms of equations)

Answer 1

Ex. given the moment of inertia of the platform, and ini. angular velocity, and r distance. inivel of block is 0

Answer 2

Assuming that the block is sufficiently heavy or the coefficient of friction is sufficiently large, it will remain stationary with respect to the rotating platform and the moment of inertia simply increases
\[I = I_0 + m_{block}\cdot r^2\]
In the absence of external torques, angular momentum is conserved, which means that
\[I_0 \omega_0 = I_f\omega_f =(I_o + m_{block}\cdot r^2)\omega_f \]
so
\[\omega_f = \left(\frac{I_0}{I_0 + m_{block}\cdot r^2}\right) \cdot \omega_0\]

Answer 3

Obviously if the surface is so slick that friction doesn't play a role, or the object is so light that it just slides off (like a ping pong ball or something) this no longer holds true, but I assume this is not the situation to which you are referring.