Question

A Cylinder is given ang,velo. x & kept on horizontal rough surface the initial velo. was 0 . Find distance travelled by cylinder before it performs pure rolling and work done by friction force?

Answer 1

Fr Vincent is going to tackle this one, I hope.

Answer 2

Forward friction force is constant as long as slipping occurs.
There might be a faster way, but here is what I would do:

- Writing down N's 2nd law will lead to velocity of centre \(v(t)\)
- Writing down net torque = I alpha will lead to angular velocity \(\omega(t)\)

Equating \(v=R\,\omega\) will lead to time until pure rolling starts.

Answer 3

Answers should be:

\(t_{rolling}=\dfrac{R\,\omega_o}{3\mu\,g}\)

\(dist.=\dfrac{R^2\omega_o^2}{18\mu\,g}\)