A pair of involute spur gears having 20 and 40 teeth are in mesh, the speed of smaller wheel being \(2000 \mathrm{rpm}\). Calculate the sliding velocity between gear teeth faces

(a) at the point of engagement,

(b) at the pitch point, and

(c) at the point of disengagement, if smaller wheel is the driver. Pressure angle is \(20^{\circ}\), addendum \(=5 \mathrm{~mm}\), and module \(=5 \mathrm{~mm}\).

Also find the angle turned through by the pinion while any one pair of teeth is in contact.