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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