An object consists of a rod (of length 3.00 m and negligible moment of inertia)to which four small 3.50-kg masses are attached,one at each end and one at each point on the rod spaced at 1.00-m intervals.The moment of inertia of this object about an axis perpendicular to the rod and through one of the end masses: A)is 49 kg·m². B)is 21 kg·m². C)is 31.5 kg·m². D)is 10.5 kg·m². E)cannot be uniquely determined until it is stated which inner mass the axis goes through.

Question

Quizplus · Accepted Answer

The moment of inertia of a rod about an axis perpendicular to the rod and through one of the end masses is 1/3 ML^2, where M is the mass of the rod and L is its length. The moment of inertia of each of the four small masses about the same axis is 1/2 mr^2, where m is the mass of each small mass and r is the distance from the axis to the center of mass of each small mass. The total moment of inertia of the object about the given axis is therefore:I = (1/3)ML^2 + 4(1/2)mr^2= (1/3)(3.50 kg)(3.00 m)^2 + 4(1/2)(3.50 kg)(1.00 m)^2= 49 kg·m^2

An Object Consists of a Rod (Of Length 3