Question

How does the center of mass come into play when you are trying to determine if something is balanced? At what point will and object rotate or fall over?

Answer 1

Center of mass is the center for all the massed particles. This can be explained as If a force is applied on an object each massed particle may move in any direction, but the point which explains the translational motion of the object is center of mass.

Center of mass explains the translational motion of all particles.

If a force is applied about a point the moment of force produces rotational motion. The point which explains about rotational equilibrium is center of gravity.

For a symmetric uniform mass distribution this two points coincides and the point is at geometric center

For any object if center of gravity is above the center of mass it produces the unballing condition and it rotate.