# Rotatory motion of uniform disk

Consider a uniform disk rolling without slipping with a certain constant angular velocity.Firstly it is moving in sufficiently rough surface.What will happen if it crosses the rough surface and just enters the smooth frictionless surface in its way?Will it be in the state of pure rotation or attains translatory motion or remains in pure rolling state.Please explain.

## 1 Answer

Note that friction opposes (or tends to oppose) relative motion and ceases to act when there is no tendency of relative motion. Friction acts on lower point of disc till it comes at rest with respect to ground.

With respect to ground the lower point can considered as superposition of 2 velocities : $v_{cm}$ (linear) and $w_{cm}R$(due to rotation of disk about centre) in opposite directions where $cm$ stands for centre of mass of disc which is its centre(here).

Friction provides force and torque to adjust them together till $v'=w'R$ where v' and w' are new speeds and angular speeds respectively.

Now no friction acts. So, would it matter if friction can act or not? $NO.$

• You mean that it will always be in state of pure rolling – Deepanshu Feb 25 '14 at 16:13
• @Deepanshu In the conditions you mentioned, yes. – evil999man Feb 25 '14 at 16:14