Definition
Definition of Center of Mass
COM is a single point that tracks the average location of mass.
- Weighted average
- Vector position
- Physical intuition
Momentum & Collisions · Physics
Center of Mass
The center of mass is the weighted “average position” of mass: \(\vec r_{cm}=\frac{1}{M}\sum m_i\vec r_i\).
This topic includes
Subtopics to master
Compute COM for particles, continuous bodies, and use symmetry to simplify.
Discrete
COM for Discrete Particles
Use \(\vec r_{cm}=\frac{1}{M}\sum m_i\vec r_i\) and apply components.
- 1D, 2D, 3D
- Component method
- Worked setups
Continuous
COM for Continuous Systems
Replace sums with integrals: \(\vec r_{cm}=\frac{1}{M}\int \vec r\,dm\).
- Density idea
- Line/area/volume mass
- Setup strategy
Shortcut
Symmetry and Center of Mass
Symmetry can locate COM instantly (or reduce integrals massively).
- Mirror symmetry
- Uniform objects
- Composite shapes
Practice
Practice & Exercises
Build fluency with COM computations and symmetry reasoning.
- Discrete COM drills
- Continuous setup practice
- Composite-body problems
- Symmetry spot-check quizzes
- COM interpretation questions