Rotating Rod

Classical Mechanics Level 5

A uniform rod of mass \( m = 2015.2016 \text{ gm}\) is placed on a rough table with \(\dfrac13 \) of its portion on the table. A point mass of equal mass is attched to its end that is in air. Then the system is left alone.

Observation: We see that the rod starts sliding when it makes an angle \(\theta\) with the horizontal (measured clockwise).

What is the coefficient of friction \(\mu\) of the table.

Details and Assumptions:

  • The length of the rod is \( L = 2016.2017\text{ cm}\).

  • Given, \( \tan\theta = \dfrac {1}{12}\).

  • The point mass is attached to the right end of the rod.

  • Take \( g = 9.8\text{ m/s}^2\).

Inspiration: Aditya Kumar.
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