Question

prove the rotation v=w*r

Answer 1

v = linear speed
ω = angular speed
r = radius.

Now to prove that v = ωr:

1. By definition, ω = dθ/dt
2. By definition, θ is the ratio of the arc length (s) to the radius; that is: θ = s/r, or s=rθ
3. By definition, v = ds/dt.

From the above facts we get:

v = ds/dt
= d(rθ)/dt
= r(dθ/dt) (assuming r constant)
= rω
= ωr