A wheel rolls on a horizontal path with uniform velocity. Prove that the velocity of any point on the circumference of the wheel with respect to its centre is equal to the velocity of the wheel. What will be the instantaneous velocity of the point on the wheel which touches the ground?

Explanation

If the radius of the wheel is r then its circumference = `2pi` r, and velocity of the wheel = `(2pi r)/(T) = (2 pi r)/((2 pi)/(omega)) = omega` r ,
here, `omega` = angular velocity of the wheel.
Again, the linear velocity of any point on the circumeference of the wheel with respect to its centre is , v = `omega`r. so, this velocity is the same as the velocity of the wheel.
At any moment, when a point on the wheel touches the ground, its linear velocity with respect to the centre of the wheel is v and its direction is just opposite to the direction of the linear velocity v of the wheel. Hence, the instantaneous resultant velocity of the point on the wheel which touches the ground = v - v = 0.