Rolling is cool! - 2

A uniform solid cylinder of mass \(m = 2\text{ kg}\) is given and angular velocity of \( \omega = 5\text{ rad/sec} \) and is dropped from a height of \(h = 22 \text{ m}\) on a rough floor at \(t = 0 \).

It collides with the sufficiently rough ground such that its velocity in the vertical direction reduces to zero.

Find the time, \(t\) (in seconds) after which it starts pure rolling.

Details and Assumptions:

  • Coefficient of friction of ground is \(\mu = 0.2\).

  • Radius of cylinder is \( R = 2 \text{ m}\), \( g = 10\text{ m/s}^2\).

  • Initial height measured is of centre of mass of cylinder from ground.

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