Free Rolling and Circular Motion

This applet shows the positon, velocity and acceleration vectors

• of a point on the rim of a body rolling without slipping

  on a stationary surface.

1. 1. The term freely rolling means that there is no slipping (v=rw)
   1. at the point of contact with the ground

      --no skidding (v>rw) and no spinning in place (w>v/r),

      where v,r and w are the linear speed, radius and

      1. the angular speed of the rolling body.

   2. The center of the wheel has a linear speed (with respect to ground)

   1. equal to that of any point on its rim (with respect to center).

   3. For circular motion (in the reference frame

   1. 1. moving with the velocity of the center of the rolling body) :

      The acceleration a of a point always points in a direction

      1. opposite the position vector r,

      and the velocity vector V is perpendicular to both of them.

   4. Observe the velocity vectors of a point on the rim

   1. 1. of the rolling body.

      The white vector represents the velocity of the center

      1. with resepect to ground and

      the red vector represents the velocity of the point

      1. with respect to the center.

      The sum of these two vectors is the cyan vector

      1. representing velocity of the point relative to ground.

   5. The green curve shows the trajectory of a point on the rim.