How does the straight-line speed of the center-of-mass compare to the rotational speed of a point on the edge of the wheel? If the wheel has a constant angular velocity, the rotational speed is:

vr

=

2 π r T

When a wheel rolls without slipping, the straight-line distance traveled by the wheel's center-of-mass (in red on the simulation) is exactly equal to the rotational distance traveled by a point on the edge of the wheel (in green).

Because the distances and times are equal, the translational speed of the center of the wheel equals the rotational speed of a point on the edge of the wheel.