Today one of my friends was arguing that pure rolling can be obtained even in the absence of friction. He said that if we give translational and rotational velocity to a ball on a frictionless surface so that the net velocity at its lowermost point(the point which is in contact with ground) becomes zero.

 

Example in the given figure- If we take V,W such that V=RW, then the lowermost point will come at instantaneous stop and ball can roll about it.

When a body is rolling with slipping, friction is neccesary to bring it to pure rolling.

The net aim of friction is to make the body attain pure rolling motion

so if we take a wheel in our hand rotate it such that v = rw and then keep it on the floor

friction will do nothing as the body is already in pure rolling motion.

 

 

 

for pure rollig what you need is that there be no relative motion between the contact points.

when a disc of radius R rolls with an accl^n a (of COM) and  the disc moves with angular accl^n @

 

every point on the disc moves with a tangential accl^n of @R.

At contact point , let the accl^n be a'

So a' = a - @R

If motion is pure rolling, by def^n of pure rolling...

a' = 0

or a = @R

This is the condition of  pure rolling.

 

 

for pure rollig what you need is that there be no relative motion between the contact points.

when a disc of radius R rolls with an accl^n a (of COM) and  the disc moves with angular accl^n @

 

every point on the disc moves with a tangential accl^n of @R.

At contact point , let the accl^n be a'

So a' = a - @R (see figure)

If motion is pure rolling, by def^n of pure rolling...

a' = 0

or a = @R

This is the condition of  pure rolling.

 

Now if the surface is rough,

frictional force for rolling WITH slipping exists

 

 

but frictional force for rolling WITHOUT slipping may or may not exists (i,e, may be zero )

 

 

whatever may be the case............ you must remember that for pure rolling .... there should not be relative motion between the contact points.

hey

since the body is rolling the point of contact will be at instaneous rest with respect to the surface.... so no motion tendency ... so no friction

as simple as it is

cheers

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