Question

The thin uniform rod in the figure has length 5.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest at angle θ = 50° above the horizontal. Use the principle of conservation of energy to determine the angular speed of the rod as it passes through the horizontal position. Assume free-fall acceleration to be equal to 9.83 m/s2.

Answer 1

mechanical energy at point A is only potential

where:
It is the acceleration of gravity
  It is the mass of the bar

  It is the height of the center of mass and is calculated as follows

mechanical energy at point B is only rotational kinetic, is given by:

where

  moment of inertia A rod with respect to an end

  angular velocity

as the mechanical energy is constant

replacing

simplifying m

expression for the angular velocity

evaluated numerically