Impulse and momentum change calculator

Impulse J = F * delta_t (in N*s) is the product of force and the time over which it acts. It measures the cumulative effect of a force — important in collisions, shots and impacts where contact time is brief.

The impulse-momentum theorem states that impulse equals change of momentum: J = delta_p = m * delta_v. Therefore F * delta_t = m * delta_v. It links the force-time product to the resulting change in motion.

Momentum p = m * v (kg*m/s) is the product of mass and velocity. It is a vector quantity. The total momentum of an isolated system is conserved (law of conservation of momentum).

For a given impulse J, F = J / delta_t. Shorter contact time means greater average force. Airbags extend collision time to reduce the peak force on the driver for the same overall impulse.

In a system with no external forces, total momentum is constant. Collision of two balls: m1*v1 + m2*v2 = const. Fundamental in mechanics, astrophysics and nuclear physics.

Force F (N) is the instantaneous interaction. Impulse J = F * delta_t accounts for both magnitude and duration. Two force-time combinations can give the same impulse: 100 N for 1 s = 50 N for 2 s.

For a constant force J = F * delta_t. For a time-varying force J = integral of F(t) dt from t1 to t2. As an approximation, use average force: J = F_avg * delta_t.

In quantum mechanics momentum is an operator: p = -i*hbar*(d/dx). Heisenberg's uncertainty principle states delta_x * delta_p >= hbar/2. This is distinct from classical momentum m*v.

Kicking (football, tennis, baseball): force F and contact time delta_t (typically 1–50 ms) are measured. High force over short contact gives large impulse and ball speed. High-speed video allows precise measurement of both.

Impulse J = F * delta_t (N*s) involves force and time; its result is a change of momentum. Work W = F * delta_s (J) involves force and displacement; its result is a change of kinetic energy. They are distinct physical quantities.