#198. Moment of inertia about center of a segmented bar A bar of width is formed of three uniform segments with lengths and areal densities given by: Matlab/Mathematica input: L1 = 6 rho1 = 1 L2 = 6 rho2 = 8 L3 = 4 rho3 = 5 What is the moment of inertia of the bar about the center of mass ?

Complete Complete

The complete question is shown on the first uploaded image

The moment of inertia of the bar about the center of mass is

Explanation:

The free body diagram  is shown on the second uploaded image

From the diagram we see that is

The mass of each segment is

The distance from the origin to the center of the segments i.e the center of masses for the individual segments

The  resultant center of mass is mathematically evaluated as

The moment of Inertia of each segment of the bar is mathematically evaluated

              =            

               =    

               =            

According to parallel axis theorem the moment of inertia about the center () is mathematically evaluated as

answer:

the answer is d

explanation: