A large drum having radius R is spinning around its axis with angular velocity $$\omega$$, as shown in figure. The minimum value of $$\omega$$ so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M as $$\mu$$, is :

To keep the mass stuck to the wall, three primary forces are at play:

Normal Force ($$N$$): Acts horizontally toward the axis, providing the centripetal force $$\longrightarrow\ $$ $$N = M\omega^2R$$

Weight ($$Mg$$): Acts vertically downward.

Friction ($$f$$): Acts vertically upward to oppose the weight $$\longrightarrow\ $$ $$f = Mg$$

The friction force is limited by the coefficient of friction ($$\mu$$):

$$f \leq \mu N$$

$$Mg \leq \mu(M\omega^2R)$$

$$g \leq \mu\omega^2R$$

$$\omega^2 \geq \frac{g}{\mu R}$$

$$\omega_{min} = \sqrt{\frac{g}{\mu R}}$$