torque and equilibrium

Question

What is the difference between center of mass and center of gravity? How they related to torque and equilibrium?

Answer 1

Mass is a constant. As such the center of mass is the point at which all of the mass is centered...For a sphere of 2 kg and a sphere of 1 kg separated by a distance of 1 meter, the center of mass is located roughly where the two plusses are...the below is a schematic. Because the 2x mass has more mass the center of mass is closer to it by the ratio of the masses and the distance... 

 

x - - - - - - -++ - - 2x

 

Center of gravity is dealing with forces. F = m*a

 

The acceleration of certain parts of the system of masses may be different. In that case, there will be a rotational movement around the center of gravity. Torque is just the angular equivalent of F = ma (but in cylindrical coordinates when dealing with a 2D world).

 

 

When the center of gravity is in equilibrium, it means that all the forces (or the torque around the center of gravity point) are equal and thus no angular movement takes place.

 

For a system where the distance between the objects is much less than the distance that the force field you are in varies then the center of mass and center of gravity are equal...think of two bowling balls near the surface of the earth. Here for our world, they are the same...on the cosmos level though they are not. That is the difference...