What is the displacement of the centre of the wheel in one rotation? Let the radius of the wheel be R ?

2πR

 Let the time taken for one rotation be ‘T’. Let the angular speed of the wheel be ‘ω’.

$\omega = \frac{2\pi}{T}$

The velocity of the centre is $ V_c = \omega R = \frac{2\pi}{T} \times R$

∴ Displacement of centre in one rotation is $ S =  V_c T = 2\pi R$