A block of mass m is placed on a horizontal ruler. The coefficient of friction between the block and the ruler is . The ruler is fixed at one of its ends, and the block is situated at a distance L from this fixed end. The ruler undergoes rotation in the horizontal plane about the fixed end. Determine the maximum angular speed such that the block does not slip.

Step-by-step solution

When the ruler rotates in the horizontal plane, the block moves in a circular path of radius L . The necessary centripetal force for this circular motion is provided by the static friction between the block and the ruler. The centripetal force required is F_c = m ^2 L . The maximum static frictional force available is f_ = N = m g . For the block not to slip, the required centripetal force must be less than or equal to the maximum static friction: m ^2 L m g ^2 g L g L Thus, the maximum angular speed is g L .