Question

1. Center of Mass Let's start with the following two shapes. Where is their center of mass - that is, around what point would they balance? Or around what point would they freely spin?" 4 identical uniform spheres connected by massless rods Ring of uniform density Io 1. "That's easy," you say, "the center of mass is at the center." "But wait," your friend speaks up, "that doesn't make sense. These objects have no mass at the center, so there isn't any center of mass for these objects." How do you reply to your friend?

Answer 1

The point o is the center of mais of the system constructed by : 4 identical uniform spheres, & The point c which is the center of the ring of uniform density, in the center of mass.

1 The definition of mass of a system of with nespect to some Chosen onigine is center of particles suitably & min Rema here oi is the position of i'th particle with mass mit we have no particle Systen. The position of Center of mass is a Geometrie quantity that depends upon the mass disto, bution e the choice of onigine. It is not necessary to have some muss at the psition of center of mass. The all you can say that is you apply some force, & if the line of action of your force passes through the center of mass then

the system translational undergoes Pure motion (with no notation) E miñiz which implies the moment of mass of the system is zero vector, ie, the mass is symmetrically distributed about the origine, but there may be no mass point Pluced night on the origin the all it requirs to Rom become zero is the symmetric distribution of mass with respect to origine.