Chapter 7

• Momentum is a vector symbolized by the symbol p, and is defined as the rate of change of momentum is equal to the net force:
• The total momentum of an isolated system of objects remains constant.
• In an elastic collision, total kinetic energy is also conserved.
• The center of mass of a system is the point at which external forces can be considered to act.
• In an inelastic collision, some kinetic energy is lost.
• In a completely inelastic collision, the two objects stick together after the collision.
• Momentum conservation works for a rocket as long as we consider the rocket and its fuel to be one system, and account for the mass loss of the rocket.
• During a collision, objects are deformed due to the large forces involved.
• The force is equal to the change in momentum divided by time, so the definition of impulse is:
• The impulse tells us that we can get the same change in momentum with a large force acting for a short time, or a small force acting for a longer time.
• Momentum is conserved in all collisions.
• Collisions in which kinetic energy is conserved as well are called elastic collisions, and those in which it is not are called inelastic.
• In an elastic collision, both momentum and kinetic energy are conserved, so two equations can be written.
• This allows us to solve for the two unknown final speeds.
• With inelastic collisions, some of the initial kinetic energy is lost to thermal or potential energy.
• A completely inelastic collision is one where the objects stick together afterwards, so there is only one final velocity.
• Conservation of energy and momentum can also be used to analyze collisions in two or three dimensions, but unless the situation is very simple, the math quickly becomes unwieldy.
• A moving object collides with an object initially at rest.
• Knowing the masses and initial velocities is not enough; we need to know the angles as well in order to find the final velocities.
• The center of mass of the leg (circled) will depend on the position of the leg.
• The center of gravity can be found experimentally by suspending an object from different points.
• The sum of all the forces acting on a system is equal to the total mass of the system multiplied by the acceleration of the center of mass.
• If the collision is elastic, conservation of kinetic energy should also be applied.
• The general motion of an object can be considered as the sum of the translational motion of the CM, plus rotational, vibrational, or other forms of motion about the CM.
• This is particularly useful in the analysis of separations and explosions; the center of mass (which may not correspond to the position of any particle) continues to move according to the net force.
• External forces can be ignored in short collision times.
• The center of mass (CM) is the point that moves in the same path a particle would take if subjected to the same force as the diver.
• The center of gravity is the point where the gravitational force can be considered to act.
• High jumpers have developed a technique where their CM actually passes under the bar as they go over it, allowing them to clear higher bars.
• For two particles, the center of mass lies closer to the one with the most mass: where M is the total mass.
• Momentum conservation applies in one dimension for each subsystem.
• The total momentum of a system of particles is equal to the product of the total mass and the velocity of the center of mass.
• Complex systems can be analyzed using subsystems where one or more conservation laws apply.