Wheel moving at constant speed and no slip

Wheel moving at constant speed and no slip. What is relation of center of mass velocity and angular velocity?

The center of the wheel moves at v_c; in one revolution of the wheel the rim travels 2pR which is also the distance that the wheel is displaced.

Let T be the period of the rotational motion (time for one revolution).

If f is the frequency, T = 1/f.

OK, are you ready??:

v_c = Displacement/time = 2pR/T = R (2p/T)

= R 2pf

BUT 2pf = w. Therefore, v_c = Rw.