# Can pure rolling be reduced to pure rotation?

Can pure rolling be reduced to pure rotation?

What I concluded is that 'In pure rolling ,rigid body is in pure rotation about the instantaneous axis of rotation. So in this context it can be said that pure rolling can be reduced to pure rotation.

Am I correct?

• What do you mean by "pure rolling " or "pure rotation" Feb 6, 2021 at 7:56

Can pure rolling be reduced to pure rotation?

Yes

In which circumstances pure rolling be reduced to pure rotation?

Such a circumstance where we can apply an external force.

Let a disc be translating with velocity $$v$$ and have an angular velocity $$\omega$$ with a condition $$v=\omega R$$. Where $$R$$ is the radius. On a frictionless surface.

Initially, the disc is purely rolling, and now an external force is applied to the disc to bring it to a complete stop. Now the disc is purely rotating.

This is one such scenario that comes to mind , The reason an external force is required is that this disc would be violating the conservation of momentum if it had stopped translating in the absence of external force.