# Rolling is cool! - 2

A uniform 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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