A massless rod of length L connects three iron masses. If the first mass (at x=0) has a mass of 1.90 kg and the second mass (at x=L) has a mass of 8.77 kg and the third mass (located at the center of mass of the system) has a mass of 148 kg, what is the moment of inertia I for the free rotation about the center of mass?
The Attempt at a Solution
I= Sum(mi(ri^2)) = 1.9(0^2) + 8.77(L^2) + 148(r_cm^2)
Now i'm assuming i'm going to be wanting to find what r_cm is (it'll probably be a function of L)
To find the center of mass for i have to take an integral? or is there another way to solve this??
This isn't a uniform rod because of the different weights of the masses correct?