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  • An impulse is applied to a ring of mass m along the line passing through its centre.

An impulse is applied to a ring of mass m along the line passing through its centre.The ring is placed on a rough horizontal surface.What is the linear velocity of the centre of ring once it starts rolling without slipping.

Answers (1)

The linear velocity of the centre of the ring once it starts rolling without slipping is:

\tau =I\alpha\\\tau=fr=\mu mgr\\\Rightarrow \alpha =\frac{\mu g}{r}\\\omega _0=\omega _0+\alpha t=\frac{\mu gt}{r}\\ring\ stop\ sliding\ when\ v=\omega r\\v_0-\mu gt=\frac{\mu gt}{r}r\\v_0=2\mu gt\\v_0=p/m\ t=\frac{p}{2\mu mg}\\v=v_0-\mu gt=2\mu g\frac{p}{2\mu mg}-\mu g\frac{p}{2\mu mg}=\frac{p}{2m}

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Safeer PP

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