If you take a cotton reel and hold the end of the cotton, then you roll the reel across the ground, the cotton will unwind from the reel. Each time the reel turns once, the length of cotton unrolled is equal to the circumference of the reel.
The same holds for a bicycle or car wheel of radius
As the wheel turns once, assuming it does not slip, the distance travelled is equal to the circumference,
Suppose then that a bicycle wheel has a radius of 40 cm or 0.4 metres. As it turns once, it travels a distance equal to
metres.
If the bicycle travels a kilometre, travelling 2.513 metres with each rotation, then in turning
times, it must travel a distance
metres. Equate this to 1000 to obtain
and solve to give
rotations.