First slide

Circular motion in horizontal plane

Question

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1m. 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 is axis, will be

Moderate

A

10 rad/s
B

10π rad/s
C

$\large \sqrt {10} rad/s$
D

$\large \frac {10}{2\pi}rad/s$

Solution

For equilibrium of the block limiting friction
$\large {f_L} \ge mg \Rightarrow \mu N \ge mg \Rightarrow \mu mr{\omega ^2} \ge mg$
$\large \omega \ge \sqrt {\frac{g}{{r\mu }}} \Rightarrow {\omega _{\min }} = \sqrt {\frac{g}{{r\mu }}} \Rightarrow {\omega _{\min }} = \sqrt {\frac{{10}}{{0.1 \times 1}}} = 10\,rad/s$

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