Question

A showgirl connects two batons together at their centers to form an X. What is the moment of inertia of the combination about an axis through the center if each baton was 1.2 m long and each ball at the end of each baton has a mass of 0.25 kg (assume negligible mass in the rods)?

Answer 1

Given:

1. mass of each balls=m1=m2=0.25kg

2.Length of baton=1.2m

3.Mass of baton= negligible

To find:Moment of inertia of the combination about an axis through the center:

1.MOI= M L²/ 12 + 2 m (L/2)²  

Where, M- mass of the baton= 0 (Negligible mass as given)

  m-mass of each ball=0.25kg

  L-length of the baton=1.2m

MOI= M L²/ 12 + 2 m (L/2)2

= 0+(2x 0.25)(1.2/2)²

=0.18 Kgm²

b.Moment of inertia about an axis parallel to bar through both the balls is zero because center of mass of bar and balls lie on the axis of rotation.