# Friction +Differential Torque+Time = No motion

A square plate of side $$a$$ having surface mass density $$\sigma$$ is placed on a rough surface. Initially angular velocity $$\omega_0$$ about axis perpendicular to plane and passing through center of mass is given then plate takes time $$t$$ to come to rest. If we provide same $$\omega_0$$ about axis perpendicular to plane and passing through one of the corner then plate takes time $$Nt$$ to come to rest. Find out the value of $$N$$.

Coefficient of Kinetic Friction is $$\eta$$.

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