Rolling of a cylinder

Classical Mechanics Level 2

A solid cylinder of mass 20kg and radius 0.12metres rotating with initial angular speed of 125rad/s is placed lightly (without any transitional push) on a horizontal table with coefficient of kinetic friction = 0.15 between cylinder and table.Find out after how long the cylinder stars rolling.

3.2 3.4 3.9 4.1

Aritra Banerjee by Aritra Banerjee , 17, India

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1 solution

Steven Chase
Dec 27, 2018

Condition for rolling without slipping:

v = R ω 0 + v ˙ t f = R ( ω 0 + ω ˙ t f ) μ M g M t f = R ( ω 0 − μ M g R 1 2 M R 2 t f ) μ g t f = R ω 0 − 2 μ g t f t f = R ω 0 3 μ g ≈ 3.4 v = R \, \omega \\ 0 + \dot{v} \, t_f = R (\omega_0 + \dot{\omega} \, t_f) \\ \frac{\mu \, M \, g}{M} \, t_f = R \Big(\omega_0 - \frac{\mu \, M \, g \, R}{\frac{1}{2} M R^2} \, t_f \Big) \\ \mu \, g \, t_f = R \, \omega_0 - 2 \, \mu \, g \, t_f \\ t_f = \frac{R \, \omega_0}{3 \, \mu \, g} \approx 3.4

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Thanks for the solution.

Aritra Banerjee - 2 years, 5 months ago

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It was a nice problem. I’d like to do another one where the friction coefficient varies over distance. Let me know if you want to post that one. Otherwise, I will.

Steven Chase - 2 years, 5 months ago

I've posted a follow up problem

https://brilliant.org/problems/rolling-cylinder-part-2/

Steven Chase - 2 years, 5 months ago

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