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College Physics

Introduction to Linear Momentum and Collisions

College PhysicsIntroduction to Linear Momentum and Collisions

Rugby players colliding during a rugby match.
Figure 8.1 Each rugby player has great momentum, which will affect the outcome of their collisions with each other and the ground. (credit: ozzzie, Flickr)

Chapter Outline

8.1 Linear Momentum and Force
  • Define linear momentum.
  • Explain the relationship between momentum and force.
  • State Newton’s second law of motion in terms of momentum.
  • Calculate momentum given mass and velocity.
8.2 Impulse
  • Define impulse.
  • Describe effects of impulses in everyday life.
  • Determine the average effective force using graphical representation.
  • Calculate average force and impulse given mass, velocity, and time.
8.3 Conservation of Momentum
  • Describe the principle of conservation of momentum.
  • Derive an expression for the conservation of momentum.
  • Explain conservation of momentum with examples.
  • Explain the principle of conservation of momentum as it relates to atomic and subatomic particles.
8.4 Elastic Collisions in One Dimension
  • Describe an elastic collision of two objects in one dimension.
  • Define internal kinetic energy.
  • Derive an expression for conservation of internal kinetic energy in a one dimensional collision.
  • Determine the final velocities in an elastic collision given masses and initial velocities.
8.5 Inelastic Collisions in One Dimension
  • Define inelastic collision.
  • Explain perfectly inelastic collision.
  • Apply an understanding of collisions to sports.
  • Determine recoil velocity and loss in kinetic energy given mass and initial velocity.
8.6 Collisions of Point Masses in Two Dimensions
  • Discuss two dimensional collisions as an extension of one dimensional analysis.
  • Define point masses.
  • Derive an expression for conservation of momentum along x-axis and y-axis.
  • Describe elastic collisions of two objects with equal mass.
  • Determine the magnitude and direction of the final velocity given initial velocity, and scattering angle.
8.7 Introduction to Rocket Propulsion
  • State Newton’s third law of motion.
  • Explain the principle involved in propulsion of rockets and jet engines.
  • Derive an expression for the acceleration of the rocket and discuss the factors that affect the acceleration.
  • Describe the function of a space shuttle.

We use the term momentum in various ways in everyday language, and most of these ways are consistent with its precise scientific definition. We speak of sports teams or politicians gaining and maintaining the momentum to win. We also recognize that momentum has something to do with collisions. For example, looking at the rugby players in the photograph colliding and falling to the ground, we expect their momenta to have great effects in the resulting collisions. Generally, momentum implies a tendency to continue on course—to move in the same direction—and is associated with great mass and speed.

Momentum, like energy, is important because it is conserved. Only a few physical quantities are conserved in nature, and studying them yields fundamental insight into how nature works, as we shall see in our study of momentum.

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