# Rotating cone.

**Classical Mechanics**Level 2

A solid uniform cone having height and radius \(R\) both, is given an angular velocity \(\omega_{0}\) about its symmetry axis without any translational velocity, and its base kept on a surface having coefficient of kinetic friction \(\mu_{k}\). Find the the time **in seconds** after which its stops rotating.

**Details and assumptions**

- \(R = 49 \text{ cm}\)
- \(\omega_{0} = 20\text{ rad/s}\)
- \(\mu_{k} = 0.06\)
- \(g = 9.8\text{ m/s}^2\)