Newton actually stated his second law of motion in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes. Recall our study of Newton’s second law of motion ( F net = m a). Force influences momentum, and we can rearrange Newton’s second law of motion to show the relationship between force and momentum. Momentum is so important for understanding motion that it was called the quantity of motion by physicists such as Newton. Since mass is a scalar, when velocity is in a negative direction (i.e., opposite the direction of motion), the momentum will also be in a negative direction and when velocity is in a positive direction, momentum will likewise be in a positive direction. Momentum is a vector and has the same direction as velocity v. A large, fast-moving object has greater momentum than a smaller, slower object. ![]() Therefore, the greater an object’s mass or the greater its velocity, the greater its momentum. © Texas Education Agency (TEA).You can see from the equation that momentum is directly proportional to the object’s mass ( m) and velocity ( v). We recommend using aĪuthors: Paul Peter Urone, Roger Hinrichs Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Changes were made to the original material, including updates to art, structure, and other content updates. Want to cite, share, or modify this book? This book uses theĪnd you must attribute Texas Education Agency (TEA). With the chosen coordinate system, p yis initially zero and p xis the momentum of the incoming particle. Because momentum is conserved, the components of momentum along the x- and y-axes, displayed as p xand p y, will also be conserved. The best choice for a coordinate system is one with an axis parallel to the velocity of the incoming particle, as shown in Figure 8.8. The simplest collision is one in which one of the particles is initially at rest. We start by assuming that F net = 0, so that momentum p is conserved. To avoid rotation, we consider only the scattering of point masses-that is, structureless particles that cannot rotate or spin. We will not consider such rotation until later, and so for now, we arrange things so that no rotation is possible. For example, if two ice skaters hook arms as they pass each other, they will spin in circles. ![]() One complication with two-dimensional collisions is that the objects might rotate before or after their collision. But what about collisions, such as those between billiard balls, in which objects scatter to the side? These are two-dimensional collisions, and just as we did with two-dimensional forces, we will solve these problems by first choosing a coordinate system and separating the motion into its x and y components. In one-dimensional collisions, the incoming and outgoing velocities are all along the same line. The Khan Academy videos referenced in this section show examples of elastic and inelastic collisions in one dimension. ![]() When they don’t, the collision is inelastic. Here’s a trick for remembering which collisions are elastic and which are inelastic: Elastic is a bouncy material, so when objects bounce off one another in the collision and separate, it is an elastic collision.
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