Answer to Question #223383 in Mechanics | Relativity for Alex

Question

As shown in figure, there is a flat plank at rest on a very slippery surface. You have disc of radius a and mass equal to the mass of the disc (say M). You rotated the disc with an initial angular speed

and carefully placed it on the plank. The coefficient of friction between the disc and plank is #. You noticed that, finally when the slipping stops, the 50% of the total kinetic energy of the system is lost. If the plank is long enough, determine the time when slipping stops after placing the disc:

Answer 1

Both v should be the same.

$\mu gt=ω_0α -3 \mu gt \\ ω_0α= 4 \mu gt \\ t = \frac{ω_0α}{\mu g}$