A 3.0 kg rod of length 5.0 m has at opposite ends point masses of 4.0 kg and 6.0 kg(a) Will the center of mass of this system be (1) nearer to the 4.0 kg mass, (2) nearer to the 6.0 kg mass, or (3) at the center of the rod? Why?
(b) Where is the center of mass of the system?
The correct answer is (2), i.e., the center of mass will be near the 6.0 kg mass.
Because, center of mass is the point where the net mass acts, numerically it is given as,
r_cm = sum(mi*ri)/sum(mi)
where i = 1 to n, mi ...
The solution gives the correct answer to the questions concerning the center of mass for a rod system and then explains how to get it in concise, logical steps.
Finding the Center of Mass of a Nonlinear Thin Rod
A thin non-uniform rod is 4 meters in length and has a linear density D, (mass per unit length), in kg/m, which is expressed by D= 3 + 5 x in which x is the distance in meters from the zero end of the rod.
Find the x coordinate of the center of mass of the rod.