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Momentum & Collisions · Physics

Motion of the Center of Mass

The COM behaves like a single particle: \(M\vec a_{cm}=\sum \vec F_{\text{ext}}\).

This topic includes

Subtopics to master

Use the COM viewpoint to simplify explosions and collisions and connect external forces to overall motion.

Law
Net External Force & COM Motion
The COM accelerates according to external forces only.
  • \(\sum \vec F_{ext}=M\vec a_{cm}\)
  • Internal forces cancel
  • What this means physically
Start subtopicKey relationship.
Isolated
COM Motion in Isolated Systems
If \(\sum \vec F_{ext}=0\), COM moves at constant velocity.
  • Constant \(\vec v_{cm}\)
  • Momentum connection
  • Collision intuition
Start subtopicConservation perspective.
Frames
COM Frame of Reference
In the COM frame, total momentum is zero; many problems become cleaner.
  • \(\vec P=0\) in COM frame
  • Symmetry in collisions
  • Relating frames
Start subtopicPower tool.
Applications
Explosions and Collisions
Explosions change relative motion, but the COM follows external forces only.
  • Fragment motion
  • Recoil reasoning
  • COM path stays smooth
Start subtopicClassic use case.
Practice
Practice & Exercises
Use COM to simplify multi-object motion problems.
  • Compute \(\vec r_{cm}(t)\) and \(\vec v_{cm}\)
  • External-force COM problems
  • Explosion/recoil COM sets
  • Frame-change drills
  • Concept checks
Open practiceHuge simplifier.