First slide

Friction as component of Net Contact Force

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 $(g = 10 m / s^{2})$

Moderate

A

$10 πrad / s$
B

$\sqrt{10} rad / s$
C

$\frac{10}{2 π} rad / s$
D

$10 rad / s$

Solution

$To keep the block stationary, Frictional force \geq Weight μN \geq Mg Here, N = {Mω}^{2} r r = 1 m, μ = 0.1 For minimum ω, {μMω}^{2} r = Mg ω = \sqrt{\frac{g}{μr}} = \sqrt{\frac{10}{0.1 \times 1}} = 10 {rads}^{- 1}$

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