A uniform rod pivoted at its upper end hangs vertically. It is displaced through an angle of 60⁰ and then released. Find the magnitude of the force acting on a particle of mass dm at the tip of the rod when the rod makes an angle of 37⁰ with the vertical.

Question

Philoid · Accepted Answer

Given:

Length of the rod= L

Mass of the rod= m

Initial angle of displacement = 60⁰

By the law of conservation of energy

Torque acting on the rod is given as

We know, T=Iα, angular acceleration is

centrifugal force F₁ = dm (= 0.9 dmg

tangential force F₂ = dm ( = 0.9 dmg

Total Force on dm= dm

A uniform rod pivoted at its upper end hangs vertically. It is displaced through an angle of 600 and then released. Find the magnitude of the force acting on a particle of mass dm at the tip of the rod when the rod makes an angle of 370 with the vertical.