8.1 Linear Momentum and Force
- Linear momentum (momentum for brevity) is defined as the product of a system’s mass multiplied by its velocity.
- In symbols, linear momentum is defined to be where is the mass of the system and is its velocity.
- The SI unit for momentum is .
- Newton’s second law of motion in terms of momentum states that the net external force equals the change in momentum of a system divided by the time over which it changes.
- In symbols, Newton’s second law of motion is defined to be is the net external force, is the change in momentum, and is the change time.
- Impulse, or change in momentum, equals the average net external force multiplied by the time this force acts:
- Forces are usually not constant over a period of time.
8.3 Conservation of Momentum
- The conservation of momentum principle is written
- An isolated system is defined to be one for which the net external force is zero
- During projectile motion and where air resistance is negligible, momentum is conserved in the horizontal direction because horizontal forces are zero.
- Conservation of momentum applies only when the net external force is zero.
- The conservation of momentum principle is valid when considering systems of particles.
8.4 Elastic Collisions in One Dimension
- An elastic collision is one that conserves internal kinetic energy.
- Conservation of kinetic energy and momentum together allow the final velocities to be calculated in terms of initial velocities and masses in one dimensional two-body collisions.
8.5 Inelastic Collisions in One Dimension
- An inelastic collision is one in which the internal kinetic energy changes (it is not conserved).
- A collision in which the objects stick together is sometimes called perfectly inelastic because it reduces internal kinetic energy more than does any other type of inelastic collision.
- Sports science and technologies also use physics concepts such as momentum and rotational motion and vibrations.
8.6 Collisions of Point Masses in Two Dimensions
- The approach to two-dimensional collisions is to choose a convenient coordinate system and break the motion into components along perpendicular axes. Choose a coordinate system with the -axis parallel to the velocity of the incoming particle.
- Two-dimensional collisions of point masses where mass 2 is initially at rest conserve momentum along the initial direction of mass 1 (the -axis), stated by and along the direction perpendicular to the initial direction (the -axis) stated by .
- The internal kinetic before and after the collision of two objects that have equal masses is
- Point masses are structureless particles that cannot spin.
8.7 Introduction to Rocket Propulsion
- Newton’s third law of motion states that to every action, there is an equal and opposite reaction.
- Acceleration of a rocket is .
- A rocket’s acceleration depends on three main factors. They are
- The greater the exhaust velocity of the gases, the greater the acceleration.
- The faster the rocket burns its fuel, the greater its acceleration.
- The smaller the rocket's mass, the greater the acceleration.