# What is the difference between center of gravity and center of mass?

Aug 11, 2017

See below...

#### Explanation:

An unconstrained object (no axle or pivot) on which there is no net force will rotate about a point called the center of mass.

• The center of mass remains motionless while every other point on the object undergoes circular motion around it.
• The center of mass is the mass-weighted center of the object.
• The distribution of an object's mass is balanced around its center of mass.

The center of gravity is the point at which the resultant torque due to gravity disappears.

• Gravity acts on every particle in the object, exerting a downward force of magnitude ${m}_{i} g$ on a particle $\text{i}$.
• The gravitational torque is found by treating the object as if all its mass were concentrated at the center of mass .
• The point at which gravity acts is called the center of gravity
• The magnitude of the gravitational torque on a particle is $\left\mid \tau \right\mid = {m}_{i} g {d}_{i}$ where ${d}_{i}$ is the moment arm
• An object will balance on a pivot only if the center of mass is directly above the pivot point. Otherwise, the gravitational torque will cause the object to rotate.

$\therefore$ As long as gravity is uniform over the object (always true for objects on Earth), there is no difference between the center of gravity and the center of mass.