Conservation of Momentum Cheat Sheet

The core ideas of Conservation of Momentum distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

Linear Momentum

The product of an object's mass and velocity (p = mv). Momentum is a vector quantity, meaning it has both magnitude and direction. Heavier or faster objects carry more momentum.

Conservation of Momentum

In a closed system with no external forces, the total momentum before an interaction equals the total momentum after. This applies to all types of collisions and explosions.

Elastic Collision

A collision in which both momentum and kinetic energy are conserved. The objects bounce off each other without any energy being converted to heat, sound, or deformation.

Inelastic Collision

A collision in which momentum is conserved but kinetic energy is not. Some kinetic energy is converted to other forms. In a perfectly inelastic collision, the objects stick together after impact.

Impulse

The product of force and the time interval over which it acts (J = F * delta_t). Impulse equals the change in momentum of an object and explains how forces change an object's motion over time.

Center of Mass

The point representing the average position of all mass in a system, weighted by each object's mass. The center of mass moves as if all external forces act on the total mass concentrated at that single point.

Impulse-Momentum Theorem

The theorem stating that the impulse applied to an object equals its change in momentum: J = F * delta_t = delta_p. A given momentum change can be achieved by a large force over a short time or a small force over a long time.

Recoil and Explosions

When a system initially at rest separates into parts (explosion, gun firing, push-off), conservation of momentum requires the fragments to carry equal and opposite momenta. The lighter fragment always moves faster than the heavier one.

Key Terms at a Glance

Momentum (p):The product of an object's mass and velocity, p = mv. A vector quantity measured in kg m/s that describes the quantity of motion an object possesses.

Conservation Law:A fundamental principle stating that a particular physical quantity remains constant in a closed system. Momentum conservation holds when no net external force acts on the system.

Elastic Collision:A collision in which both total momentum and total kinetic energy are conserved. Objects bounce apart with no energy lost to deformation, heat, or sound.

Inelastic Collision:A collision in which total momentum is conserved but total kinetic energy is not. Some kinetic energy converts to other forms such as thermal energy and sound.

Perfectly Inelastic Collision:A special inelastic collision in which the colliding objects stick together after impact, moving as a single combined mass. This type loses the maximum kinetic energy while still conserving momentum.

Impulse (J):The product of a net force and the time interval over which it acts, J = F * delta_t. Equal to the change in momentum of the object on which the force acts.

Recoil:The backward motion of an object after it propels another object forward. Governed by conservation of momentum: the recoiling object gains momentum equal in magnitude and opposite in direction to the launched object.

Center of Mass:The mass-weighted average position of all parts of a system. In a closed system, the center of mass velocity remains constant regardless of internal forces between the parts.

Closed System:A system in which no net external force acts on the objects involved. Internal forces between objects within the system do not change the total momentum.

Kinetic Energy:The energy of motion, KE = (1/2)mv^2. Unlike momentum, kinetic energy is a scalar (no direction) and is not conserved in inelastic collisions.

Newton's Third Law:For every action force there is an equal and opposite reaction force. This law is the foundation of momentum conservation: internal forces always come in equal-and-opposite pairs, so they cancel in the total.

Ballistic Pendulum:A laboratory device that measures a projectile's speed by embedding it in a hanging block (perfectly inelastic collision) and measuring the resulting swing height. Combines momentum conservation with energy conservation.

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