Statement
Mathematical Statement
Impulse equals change in momentum.
- \(\vec J=\Delta \vec p\)
- Vector form
- Component form
Momentum & Collisions · Physics
Impulse–Momentum Theorem
A compact statement: \(\displaystyle \int_{t_i}^{t_f}\vec F\,dt = \Delta \vec p\).
This topic includes
Subtopics to master
Use the theorem to solve short-time force interactions without tracking every detail of motion.
Derivation
From Newton’s Second Law
Start with \(\sum\vec F=d\vec p/dt\) and integrate over time.
- Integration step
- Constant vs variable force
- Interpretation
Applications
Applications to Motion Problems
Solve for final speed/velocity, impulse, or average force.
- Stopping problems
- Push/launch problems
- Direction changes
Timing
Short-Time Interactions
Collisions and impacts have tiny \(\Delta t\) but large impulse.
- Why average force helps
- Peak vs average
- Area under \(F(t)\)
Practice
Practice & Exercises
Work impulse–momentum problems in 1D and 2D components.
- Impulse from graphs
- \(\Delta \vec p\) vector drills
- Average force sets
- Impact time reasoning
- Quick concept checks