First slide

Circular motion in horizontal plane

Question

A body moves along a circular path of radius 10 m and the coefficient of friction is 0.5. What should be its angular speed in rad/s if it is not to slip from the surface $(g = 9 .8 {ms}^{2})$

Moderate

A

5
B

10
C

0.1
D

0.7

Solution

For moving on circular path with the force must equal frictional force.
That is,
$\begin{array}{l} \frac{{mu}^{2}}{r} = μmg \\ \Rightarrow {mrω}^{2} = μmg [∴ u = rω] \\ \Rightarrow {rω}^{2} = μg \\ ∴ ω = \sqrt{\frac{μg}{r}} = \sqrt{\frac{0 .5 \times 9 .8}{10}} = 0 .7 rad / s . \end{array}$

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