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# 9: Linear Momentum and Collisions

• 9.1: Prelude to Linear Momentum and Collisions
The concepts of work, energy, and the work-energy theorem are valuable for two primary reasons: First, they are powerful computational tools, making it much easier to analyze complex physical systems than is possible using Newton’s laws directly (for example, systems with nonconstant forces); and second, the observation that the total energy of a closed system is conserved means that the system can only evolve in ways that are consistent with energy conservation.
• 9.2: Linear Momentum
Momentum is a concept that describes how the motion of an object depends not only on its mass, but also its velocity. Momentum is a vector quantity that depends equally on an object's mass and velocity. The SI unit for momentum is kg • m/s.
• 9.3: Impulse and Collisions (Part 1)
When a force is applied on an object for some amount of time, the object experiences an impulse. This impulse is equal to the object’s change of momentum. Newton’s second law in terms of momentum states that the net force applied to a system equals the rate of change of the momentum that the force causes.
• 9.4: Impulse and Collisions (Part 2)
Since an impulse is a force acting for some amount of time, it causes an object’s motion to change.
• 9.5: Conservation of Linear Momentum (Part 1)
The law of conservation of momentum says that the momentum of a closed system is constant in time (conserved). A closed (or isolated) system is defined to be one for which the mass remains constant, and the net external force is zero. The total momentum of a system is conserved only when the system is closed.
• 9.6: Conservation of Linear Momentum (Part 2)
• 9.7: Types of Collisions
An elastic collision is one that conserves kinetic energy. An inelastic collision does not conserve kinetic energy. Momentum is conserved regardless of whether or not kinetic energy is conserved. Analysis of kinetic energy changes and conservation of momentum together allow the final velocities to be calculated in terms of initial velocities and masses in one-dimensional, two-body collisions.
• 9.8: Collisions in Multiple Dimensions
The approach to two-dimensional collisions is to choose a convenient coordinate system and break the motion into components along perpendicular axes. Momentum is conserved in both directions simultaneously and independently. The Pythagorean theorem gives the magnitude of the momentum vector using the x- and y-components, calculated using conservation of momentum in each direction.
• 9.9: Center of Mass (Part 1)
An extended object (made up of many objects) has a defined position vector called the center of mass. The center of mass can be thought of, loosely, as the average location of the total mass of the object. The center of mass of an object traces out the trajectory dictated by Newton’s second law, due to the net external force. The internal forces within an extended object cannot alter the momentum of the extended object as a whole.
• 9.10: Center of Mass (Part 2)
• 9.11: Rocket Propulsion
A rocket is an example of conservation of momentum where the mass of the system is not constant, since the rocket ejects fuel to provide thrust. The rocket equation gives us the change of velocity that the rocket obtains from burning a mass of fuel that decreases the total rocket mass.
• 9.12: Linear Momentum and Collisions (Exercises)
• 9.13: Linear Momentum and Collisions (Summary)
• 9.14: Introduction
Linear momentum is the product of the mass and velocity of an object, it is conserved in elastic and inelastic collisions.
• 9.15: Conservation of Momentum
Net external forces (that are nonzero) change the total momentum of the system, while internal forces do not.
• 9.16: Collisions
In an inelastic collision the total kinetic energy after the collision is not equal to the total kinetic energy before the collision.
• 9.17: Rocket Propulsion
In rocket propulsion, matter is forcefully ejected from a system, producing an equal and opposite reaction on what remains.
• 9.18: Center of Mass
The position of COM is mass weighted average of the positions of particles.

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