Impulse in physics is the change in an object's momentum resulting from a force acting over a finite time interval. It is denoted by J and is equal to the product of the net average force F and the time duration Δt: J = F Δt. Equivalently, for a body of constant mass m, impulse equals the change in momentum: J = Δp = m(v2 − v1). Its directions follow the same vector sense as the applied force, so impulse is a vector quantity. Common unit representations are newton-seconds (N·s) or kilogram meters per second (kg·m/s).
Key ideas
- Relationship to momentum: Impulse is the exact change in momentum produced by the force during Δt. If the force is zero, there is no impulse and momentum remains unchanged.
- Newton’s second law linkage: The impulse delivered over a time interval corresponds to the average net external force times the interval, which equals the change in momentum.
- Short-duration, high-force events: Impulse is especially useful for analyzing collisions and impacts where forces act briefly but can produce large changes in velocity.
Common formulas
- Impulse-Force relation: J = F Δt.
- Impulse as change in momentum: J = Δp = p2 − p1 = m(v2 − v1).
- If mass varies during the interval, the general form is J = ∫ F dt, but for constant mass it reduces to J = F Δt.
Applications
- Collisions: Impulse helps predict post-collision velocities when masses and initial velocities are known, via conservation of momentum and impulse-momentum theorem.
- Safety engineering: Designs (e.g., airbags, crumple zones) aim to reduce peak force or extend contact time to lower the impulse experienced by a person, thereby reducing injury risk.
Notes
- Impulse and momentum are vector quantities; both magnitude and direction depend on the direction of the applied force.
- Units: N·s and kg·m/s are equivalent representations of impulse.
