Question

A thin, uniform rod is hinged at its midpoint. To begin with, one-half of the rod is bent upward and is perpendicular to the other half. This bent object is rotating at an angular velocity of 4.7 rad/s about an axis that is perpendicular to the left end of the rod and parallel to the rod's upward half (see the drawing). Without the aid of external torques, the rod suddenly assumes its straight shape. What is the angular velocity of the straight rod?

Answer 1

initial I = (m/2)L²/3 + (m/2)L²
where L = ½ the length of the rod, and the vertical half can be treated as a point mass.
initial I₁ = mL²(1/6 + 1/2) = 2mL²/3

final I₂ = m(2L)²/3 = 4mL²/3

from the law of conservation of momentum

intial momentum Pi = final momentum Pf

I₁₁ = I₂*₂
[2mL²/3 ]*4.7 rad/s = [ 4mL²/3 ]*₂

₂ = 4.7 / 2 = 2.35 rad/s