Free Rolling and Circular Motion

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This applet shows the positon,velocity and accelerationvectors
of a point on the rim of a body rolling without slippingon a stationary surface.

1. The term freely rolling means that there is no slipping (v=rw)

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

the angular speed of the rolling body.

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

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

3. For circular motion (in the reference frame

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

The acceleration a of a point always points in a direction

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

of the rolling body.

The white vector represents the velocity of the center

with resepect to ground and

the red vector represents the velocity of the point

with respect to the center.

The sum of these two vectors is the cyan vector

representing velocity of the point relative to ground.

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

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