A coin is placed on a disc. The coefficient o | vedclass

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Question

(C) For the coin to remain on the disc without slipping,the centripetal force required for circular motion must be provided by the static frictional f

Vedclass · Accepted Answer

$\sqrt{\frac{\mu g}{r}}$

Vedclass · Answer

(C) For the coin to remain on the disc without slipping,the centripetal force required for circular motion must be provided by the static frictional force.The normal force acting on the coin is $N = mg$.The maximum static frictional force available is $f_{max} = \mu N = \mu mg$.The required centripetal force for the coin moving in a circle of radius $r$ with angular velocity $\omega$ is $F_c = m \omega^2 r$.For the coin not to slip,the centripetal force must be less than or equal to the maximum static friction:$m \omega^2 r \leq \mu mg$Solving for $\omega$:$\omega^2 \leq \frac{\mu g}{r}$Therefore,the maximum angular velocity is $\omega_{max} = \sqrt{\frac{\mu g}{r}}$.

$A$ coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$,the maximum angular velocity which can be given to the disc,so that the coin does not slip away,is:

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