Question

A cylinder rolls without slipping over a horizontal plane. The radius of the cylinder is equal to r. Find the curvature radii of trajectories traced out by the points A and B (see Fig. 1.7).

Answer 1

Let us draw the kinematical diagram of the rolling cylinder on the basis of the solution of the problem 1.53.

As, an arbitrary point of the cylinder follow a curve, its normal acceleration and radius of curvature are related by the well-known equation