CENTER OF MASS

Definition

The location on an object where mass is balanced—there is an equal amount of mass in all directions.

In 1-dimension…xcm=x1m1+x2m2+…m1+m2+…

2 dimensions

3 dimensions

Center of gravity

The point on an object where the force of gravity can act without causing a rotation (from torque)

Near the surface of the Earth, center of mass = center of gravity

For this reason, we always model the weight of an object as being downward FROM the center of mass

Stability

Resistance to tipping over

An object is only stable if the center of gravity is over the base If you hung a plum

bob from the center of gravity, it would land over the base

Stability

An object is more stable if its center of gravity is low to the ground

An object with a wide base is more stable than an object with a narrow base