A slender uniform rod 100.00 cm long is used as a meter stick. Two parallel axes that are perpendicular to the rod are considered. The first axis passes through the 50-cm mark and the second axis passes through the 30-cm mark. What is the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis?

Question

Quizplus · Accepted Answer

The moment of inertia of a rod about an axis perpendicular to the rod and passing through its center is 1/12 ML^2, where M is the mass of the rod and L is its length. The moment of inertia about an axis parallel to the first axis and passing through a point a distance d from the center is 1/12 ML^2 + Md^2. Therefore, the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis is:I2/I1 = (1/12 ML^2 + Md^2) / (1/12 ML^2) = 1 + 12d^2/L^2Substituting d = 20 cm and L = 100 cm, we get:I2/I1 = 1 + 12(20 cm)^2/(100 cm)^2 = 1.5

A Slender Uniform Rod 100