Momentum Calculator

Momentum is a measure of an object's motion, defined as p = mv (mass times velocity). It's a vector quantity, meaning it has both magnitude and direction. Heavier objects and faster objects have more momentum. A truck moving slowly can have the same momentum as a car moving fast.

Conservation of momentum states that the total momentum of a closed system remains constant. In collisions, m1*v1 + m2*v2 (before) = m1*v1' + m2*v2' (after). This holds for all collisions regardless of whether kinetic energy is conserved.

In elastic collisions, both momentum AND kinetic energy are conserved. Objects bounce off each other (like billiard balls). In inelastic collisions, momentum is conserved but kinetic energy is not - some energy is lost to heat, sound, or deformation. In perfectly inelastic collisions, objects stick together.

For elastic collisions: v1' = ((m1-m2)v1 + 2m2*v2)/(m1+m2) and v2' = ((m2-m1)v2 + 2m1*v1)/(m1+m2). For perfectly inelastic collisions: v_final = (m1*v1 + m2*v2)/(m1+m2). These formulas come from conservation of momentum (and energy for elastic).

Momentum explains car crashes (why heavier vehicles cause more damage), sports (follow-through in golf/baseball), rocket propulsion (momentum of exhaust equals momentum gained by rocket), and safety design (airbags extend collision time to reduce force via impulse).

In a head-on collision, objects move in opposite directions, so one velocity is negative. The momenta partially cancel out. If two identical objects moving at equal speeds collide head-on elastically, they exchange velocities. In a perfectly inelastic head-on collision, they may come to rest if momenta are equal and opposite.