A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coe

Question

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : ($g = 10 	ext{ m/s}^2$)

Accepted Answer

For equilibrium of the block, limiting friction $f_L \geq mg$. Since $f_L = \mu N$ and $N = mr\omega^2$, we have $\mu mr\omega^2 \geq mg$. Thus, $\omega \geq \sqrt{\frac{g}{r\mu}}$. Substituting values: $\omega_{min} = \sqrt{\frac{10}{0.1 	imes 1}} = \sqrt{100} = 10 	ext{ rad/s}$.

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