Linear Momentum
In physics, Newton's first law of motion states that a moving body will remain in motion unless acted upon by an outside force. Similarly, a body at rest (no motion) will remain at rest unless acted upon by an outside force. This concept, called inertia, is a quality that is dependent upon the mass of the object under examination. The greater the mass of an object, the greater the force must be to oppose its inertia. A related concept is linear momentum, whose value is also determined by mass. Linear momentum, or simply momentum, is a vector quantity (having both magnitude and direction) whose value is equal to the product of the mass and velocity of an object moving in a linear (not angular) fashion. Therefore, if either (or both) the mass or velocity of an object is increased, its momentum is increased. For example, very tiny particles can have great momentum if they have immense velocity. A bullet shot from a revolver, for instance, has a large momentum. Likewise, very massive objects, such as railroad trains, have great momentum even when moving very slowly. Like inertia, the force required to oppose a body's momentum is proportional to its mass.
The central concept regarding momentum is its conservation. Conservation of momentum is the characteristic that within a system, total momentum is always the same, or constant. For example, consider a rocket being propelled upward into space by the combustion of rocket fuel. Because the fuel is consumed and ejected at high velocity in the process of propulsion, the mass of the fuel carries momentum downward, in order that momentum be conserved, the rocket acquires an equal upward momentum, which propels it into space. Further, since the mass of the rocket is decreasing due to the expulsion of fuel, the velocity will increase so that the upward momentum will stay in balance with the downward momentum of the fuel.
This concept is also important when considering collisions. In any system, total momentum equals the sum of its components. For example, in billiards, the total momentum of the cue ball and the eight ball is equal to the momentum of the cue ball plus the momentum of the eight ball. If, during the final shot of the billiard game, the cue ball collides with the eight ball to propel it toward the corner pocket, conservation of momentum ensures that the total momentum does not change. Therefore, if the eight ball was not moving, some of the momentum of the cue ball will be transferred to the eight ball so that the total momentum remains constant. Conservation of linear momentum ensures that total momentum remains constant whether the collision is elastic or inelastic. Elastic collisions involve the complete conservation of both momentum and kinetic energy (the energy of motion). The example of billiard balls striking one another is an example of nearly perfectly elastic collisions. Inelastic collisions are collisions in which conservation of total momentum still occurs, but total kinetic energy is not conserved. For instance, if two balls of clay collide with one another, momentum is conserved, but some energy of movement is lost as heat and as work involved in deforming the clay.
Conservation of linear momentum acts on the center of mass of an object. The center of mass of an object is the singular point at which all of the mass of the object is acted upon by external forces. It is as if all of the mass of the body is contained in one single point. Therefore, the total momentum of a system depends upon the velocity of its center of mass.
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