# Rotational motion

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Question

# A smooth ring of mass m and radius R = 1 m is pulled at P with a constant acceleration a = 4 m s-2 on a horizontal surface such that the plane of the ring lies on the surface. Find the angular acceleration of the ring at the given position. (in rad/s2)

Moderate
Solution

## The pseudo force acting at the CM of the ring is  which produces a torque about P given as           ${\stackrel{\to }{\mathrm{\tau }}}_{\mathrm{ps}}=-\left(\mathrm{ma}\right)\left(\mathrm{R}\right)\stackrel{^}{\mathrm{k}}$This produces an angular acceleration

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A uniform cylinder of radius R(= 3m) is spin about its axis at an angular velocity ${\omega }_{0}\left(=40\sqrt{\pi }\mathrm{rad}/\mathrm{sec}\right)$and placed between two perpendicular wall. The coefficient of friction between the walls and cylinder is $\mathrm{\mu }\left(=2\right)$ Then, 25 K turns will the cylinder make before it stops. Find the value of K.