Definition
Definition of Linear Momentum
Define momentum and interpret what it represents physically.
- \(\vec p=m\vec v\)
- Direction matters
- Units and scale
Momentum & Collisions · Physics
Linear Momentum
Momentum is a vector measure of “how hard it is to stop” motion: \(\vec p=m\vec v\).
This topic includes
Subtopics to master
Define momentum for particles and systems, then connect it to forces and energy ideas.
Vectors
Momentum as a Vector Quantity
Momentum points in the direction of velocity; components matter in 2D/3D.
- Component form
- Vector addition
- Sign conventions
Single object
Momentum of a Particle
Compute momentum for a moving particle and compare situations (mass vs speed).
- Same v, different m
- Same m, different v
- Direction changes
Systems
Momentum of a System of Particles
System momentum is the vector sum: \(\vec P=\sum \vec p_i\).
- Summation idea
- External vs internal forces (preview)
- Why systems matter
Dimensions
Units and Dimensions of Momentum
Units: kg·m/s (or N·s). Dimensional checks help catch mistakes.
- kg·m/s
- N·s equivalence
- Dimensional reasoning
Frames
Momentum and Reference Frames
Momentum depends on measured velocity, which depends on the observer.
- Relative velocity
- Same event, different \(\vec p\)
- Choosing a convenient frame
Dynamics
Rate of Change of Momentum
Net force relates to momentum change: \(\sum \vec F = d\vec p/dt\).
- Constant mass case
- Meaning of \(d\vec p/dt\)
- Bridge to impulse
Compare
Momentum vs Kinetic Energy
Momentum and kinetic energy are related but not the same; they scale differently with speed.
- \(p\propto v\)
- \(K\propto v^2\)
- Collision implications
Practice
Practice & Exercises
Build speed with momentum vectors, systems, and comparisons to kinetic energy.
- Compute \(\vec p\) in 1D/2D
- System momentum sums
- Frame-change intuition checks
- \(p\) vs \(K\) comparison sets
- Quick concept quizzes