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

##### 1 Answer

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_ig# on a particle#"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
#abs(tau)=m_igd_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.

**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.**