Question

Find the moments Mx and My and the center of mass of the system, assuming that the particles have equal mass m.

Four particles are located at points (1,3), (2,3), (3,1), (4,1).????? need help

Answer 1

so the moments of mass are going to be the ratios of the masses and their distances in their respective axis'. If we plot the points on the coordinate system we can see that for x, equal masses are occupying x = 1 through 4. with an equal density value. because they are all uniform we can intuit the moment to be the center of that distribution so Mx = 2.5. Looking at y we have two equal masses at y = 1 and another set of masses at y = 3. This means that we have a moment in between those distributions and our My = 2. The center of mass is the combination of the two, and it is at pt (2.5, 2). Because the masses considered are in general and also equal to each other, we don't really need to bother taking them into deep consideration in the Mx, My formula, it is more about intuiting how their distribution is effecting each other.