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h1. MIT 8.01 Lesson 13: Momentum
{include:Momentum (Intro)}
Newton emphasizes the linearity of momentum with both mass and velocity. He specifies our sum over different bodies by further stating that the motion of the whole is the sum of the motions of all the parts; and therefore in a body double in quantity, with equal velocity, the momentum is double; with twice the velocity also, it is quadruple.
Newton's Second Law is the fundamental law of change for momentum,
Frac{d\vecp}{dt}=\Sigma_j\vec{F_j}
Where the sum goes over all the forces acting on any body in the system.
Technically, the concept of linear momentum applies only to collections of point objects. The momentum of a rigid body is simply the sum of the momentum of each of the atoms in the body, which turns out to be the body's mass times its center of mass velocity. The momentum of a system composed of many rigid bodies and point particles is then the sum of their individual momenta, which again can be expressed as the total mass of this system times the velocity of the system's center of mass. This is true, and a valuable concept, especially when the system is composed of disparate objects going in different directions - for example a system of two cars about to have a collision, or after they have just had a collision.
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