Question

A point A is located on the rim of a wheel of radius R= 0.50 m which rolls without slipping along a horizontal surface with velocity v = 1.00 m/s. Find:

(a) the modulus and the direction of the acceleration vector of the point A;

(b) the total distance s traversed by the point A between the two successive moments at which it touches the surface.

Answer 1

(a) The plane motion of a solid can be imagined as the combination of translation of the C.M. and rotation about C.M.

In the problem v_c=v=constant, and the rolling is without slipping i.e, v_c=v=ωR

toward the center of the wheel.

(b) Let the center of the wheel move toward the right (positive x-axis) than for pure tolling on the rigid horizontal surface, wheel will have to rotate in clockwise sense. If ω be the angular velocity of the wheel then  ω=v_c/R=v/R.

Let the point A touches the horizontal surface at t=0, further let us locate the point A at t=t,