A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.70 m long and each ball on the end is 0.10 kg.(Ignore the mass of the rods. )What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons? A)2.5E-2 kg·m² B)4.9E-2 kg·m² C)7.0E-2 kg·m² D)1.4E-1 kg·m² E)7.4E-2 kg·m²

Question

Quizplus · Accepted Answer

The moment of inertia of a rod about an axis perpendicular to the rod and passing through one end is (1/3)ML^2. The moment of inertia of a point mass about an axis perpendicular to the line from the mass to the axis and passing through the mass is mr^2. The moment of inertia of the arrangement about an axis formed by one of the batons is:I = (1/3)M(0.70 m)^2 + (1/3)M(0.70 m)^2 + m(0.10 m)^2 + m(0.10 m)^2= (1/3)M(0.49 m^2) + (1/3)M(0.49 m^2) + 2m(0.01 m^2)= (2/3)M(0.49 m^2) + 2m(0.01 m^2)= (2/3)(0.20 kg)(0.49 m^2) + 2(0.10 kg)(0.01 m^2)= 0.0653 kg·m^2 + 0.002 kg·m^2= 0.0673 kg·m^2= 6.73E-2 kg·m^2Therefore, the correct answer is A.

A Majorette Takes Two Batons and Fastens Them Together in the Middle