Rotating cone.

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

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

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