Question

A disc of radius R rotates from rest about a vertical axis with a constant angular acceleration such that a coin placed at the periphery of the disc moves with a tangential acceleration a as shown in Fig. If the coefficient of static friction between the coin and disc is ${\mu }_s$, find the velocity of the coin before it starts sliding relative to the disc.

Answer 1

$\therefore$ Before it starts sliding

$\mu mg=m{\omega }^{2}R$

We know that $V=R\omega$

$\therefore \mu mg=\frac{m{V}^2}{R}\Rightarrow V=\sqrt{\mu gR}$