Momentum (physics)

In the field of physics, momentum is a measure of the motion of a physical object in terms of its mass and velocity. To adequately understand momentum, therefore, one must first understand mass and velocity. Mass is simply the amount of matter in a physical object, irrespective of its volume or any outside forces acting on it, while velocity is the rate at which an object changes position. For example, if a person takes a step forward and then steps back to their original position, that person would be said to have zero velocity. However, if a person takes multiple steps to another location and does not return to the original starting point, that person has increased their velocity.

Momentum is related to Isaac Newton’s first law of motion, which states, “Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.” In other words, an object at rest will remain at rest, and an object moving in a straight line will continue to move in that straight line, until a force such as friction, gravity, or collision with another object causes its velocity or direction to change. If no external force is applied and the object’s mass and velocity remain the same, then its momentum will remain constant.

Background

Momentum, sometimes called “linear momentum” or “translational momentum” to distinguish it from angular momentum, relates to the mechanics of how something moves. In simpler terms, it can be thought of as the force or speed of mass in motion. All objects have mass because all objects occupy space. If an object with mass moves from one location to another, even an infinitesimal distance, then that object has momentum. Thus, for an object to have momentum, it must have both mass and movement. A lighter object will have less momentum than a heavier object moving at the same speed, and a slow-moving object will have less momentum than an object of the same mass that is moving more quickly.

In a sense, momentum can be said to describe how difficult a moving object would be to stop. If a person were to throw two differently sized balls in the same direction at the same speed, the ball with the greater mass would hit its target with more force because its momentum would be greater, making it harder to stop. However, if the smaller object’s velocity were sufficiently greater, the momentum of that smaller object would be greater than a larger object traveling at a fraction of its velocity. For example, a fired bullet would have greater momentum than a thrown ball because the difference between the two objects’ masses is much smaller than the difference between their velocities.

Overview

The mathematical equation for momentum is written as p=mv, where p is momentum, m is mass, and v is velocity. Thus, the momentum of an object is directly proportional to both its mass and its velocity. The standard unit for momentum is kg·m/s, derived from the mass of the object in kilograms times its velocity in meters per second.

One of the most important laws in physics is the law of conservation of momentum, which states that an object cannot simply lose momentum. Rather, when two objects collide in an isolated system—that is, where no other outside forces can act on them—any momentum lost by one object is gained by the other object, and the sum total of their momenta remains the same. In other words, momentum is not lost, but simply transferred from one object to another. This law can be seen in action in sports such as tennis, baseball, or soccer, where the collision of one object (a racket, a bat, or a player’s foot) with another (the ball) imparts sufficient momentum to the second object to send it in another direction at speed.

Linear momentum is distinct from angular momentum, which measures the momentum of a spinning or rotating object. Angular momentum is still a function of mass and velocity, but it must account for the fact that the direction of a rotating object’s momentum is always changing. In addition, the parts of a rotating object closest to the axis of rotation move more slowly than the parts farthest away because they have less distance to travel, so the total angular momentum of an object is actually the sum of the angular momenta of each of its constituent particles. Rather than calculate the angular momentum of each particle, one can determine an object’s total angular momentum by multiplying its angular velocity (ω) by its moment of inertia (I), which is a measure of the torque, or twisting force, needed to change its angular velocity. Angular momentum is used to measure the momentum of objects in space, such as planets and stars, since these objects rotate around a more-or-less-fixed axis.

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