Rolling without slipping
The velocity of the point (in red) is shown in x and y components,
where positive x is to the right and positive y is up.
Things to think about:
- If the wheel rolls without slipping, the wheel should move
a distance equal to the circumference for every revolution. Does it?
- When the point on the wheel is at 40 cm, right at the very surface
of the wheel, what is its velocity at the instant it makes contact
with the road? This is consistent with rolling without slipping - the
point on the wheel in contact with the road should be
instantaneously at rest. The shape of the path of the point is
known as a cycloid, by the way.
- The velocity of the point at any time is the vector sum of
the translational velocity of the wheel (1.0 m/s to the right) and
the rotational velocity because of the spin. Pause the motion at
certain times to see whether that's always true. Where is the velocity
in the y direction maximum? Why?
- Do you agree with the time it takes for the wheel to
go around once?
- Setting the point position outside the wheel is a little
unrealistic, but the shape of the path followed by the point is
neat in that situation.
Created by Andrew Duffy, Boston University Physics Department.
Last update October 29, 1998