# Friction +Differential Torque+Time = No motion

**Classical Mechanics**Level 5

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 \(\eta\).