Impulzusmomentum

Impulzusmomentum, or impulse–momentum, is a concept in classical mechanics that relates the impulse delivered to a body to the resulting change in its linear momentum. The term is commonly used in Hungarian discourse to describe the integral effect of a force applied over a period of time.

For linear motion, impulse J is defined as the integral of force F over time: J = ∫ F dt. The momentum p of a particle is p = m v, and the impulse–momentum theorem states that the impulse equals the change in momentum: J = Δp = p2 − p1. In the case of constant mass, this reduces to J = F Δt and Δp = m Δv. If the mass changes during the interaction, the relation generalizes to J = Δ(m v).

This theorem is a direct consequence of Newton’s second law, F = dp/dt, and holds for any force interaction, including collisions and expulsions of thrust. It is often used in one-dimensional problems and in more general vector form, where J and Δp are vectors with the same direction as the net impulse.

The angular counterpart is the angular impulse–momentum relation: ∫ τ dt = ΔL, where τ is torque and L is angular momentum (L = r × p). The angular impulse describes how torques change rotational motion in a manner analogous to linear impulse.

Applications of impulse–momentum analysis include collision reconstruction, sports performance, vehicle safety design, and propulsion system analysis. Units of impulse are newton-seconds (N·s), while momentum is kilogram-meter per second (kg·m/s).