Momentum, Impulse and Collisions

Linear Momentum: Definition, Properties, and Relationships

Linear momentum is a fundamental physical quantity defined as the product of an object's mass and its velocity. The mathematical formula for linear momentum is p = mv. Because velocity is a directional measurement, momentum is also a vector quantity that possesses both magnitude and direction. The direction of an object's linear momentum is always identical to the direction of its velocity. If an object is at rest, its velocity is zero, and therefore an object at rest has a linear momentum of zero. In the International System of Units (SI), the unit for linear momentum is the kilogram-meter per second (kg·m/s).

The formula p = mv demonstrates direct proportionality between momentum, mass, and velocity. Doubling the velocity of a moving object doubles its linear momentum. In the same manner, doubling the mass of an object while holding its velocity constant doubles its linear momentum. Because both mass and velocity contribute equally to this product, a massive object moving slowly can possess the same momentum as a light object moving rapidly. For instance, a heavy transport truck creeping forward at a low speed can have the exact same linear momentum as a lightweight sports car traveling at high speed.

Momentum is also central to the laws of motion. Newton's second law can be formulated as the net force equaling the rate of change of linear momentum over time. When a net force acts on an object over a period of time, it alters the object's velocity, which in turn causes the object's linear momentum to change.