To mop - clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and if coefficent of friction between the mop and the floor is , the torque, applied by the machine on the mop is:
This can be calculated by using either
= perpendicular distance from origin to the line of force.
= component of force perpendicular to line joining force.
consider a strip of radius x and thickness dx
Toraue due to friction on this strip