Question

A uniform solid cylinder of radius R = 15 cm rolls over a horizontal plane passing into an inclined plane forming an angle α= 30° with the horizontal (Fig. 1.67). Find the maximum value of the velocity v_o which still permits the cylinder to roll onto the inclined plane section without a jump. The sliding is assumed to be absent.

Answer 1

Since the cylinder moves without sliding, the centre of the cylinder rotates about the point O, while passing through the common edge of the planes. In other words, the point O becomes the foot of the instantaneous axis of rotation of the cylinder. 

It at any instant during this motion the velocity of the C.M. is v₁ when the angle (shown in the figure) is β, we have