Key Concepts: Center of Mass

What is the Center of Mass?

• The center of mass (COM) is the average position of all mass in a system, weighted by mass.
• For two particles: x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂).
• The COM of a symmetric, uniform object is at its geometric center.

Motion of the Center of Mass

• The COM moves as if all external forces were applied to a single particle of total mass M at that point.
• F_ext = Ma_cm — Newton's second law for the center of mass.
• If no external forces act, the COM moves at constant velocity (or stays at rest).

Applications

• In an explosion, individual pieces fly apart, but the COM follows the same parabolic path as before the explosion.
• A high jumper arches their back so their COM passes under the bar even though their body clears it.