Glossary
Change in Momentum
The difference between an object's final and initial momentum, also known as impulse. It indicates how much an object's motion has been altered.
Example:
When a car brakes suddenly, its change in momentum is significant, as its velocity rapidly decreases from a high speed to zero.
Closed System
A system where no net external forces act upon it, meaning no mass or energy is exchanged with the surroundings in a way that affects the total momentum.
Example:
For a perfectly isolated billiard table, the colliding balls can be considered a closed system because friction and air resistance are negligible external forces.
Conservation of Momentum
A fundamental law stating that in a closed system (one with no external forces), the total momentum before an event (like a collision or explosion) is equal to the total momentum after the event.
Example:
When a rocket expels exhaust gases downward, the conservation of momentum dictates that the rocket itself gains an equal and opposite momentum upward, propelling it into space.
Elastic Collisions
Collisions in which both momentum and kinetic energy are conserved. Objects bounce off each other without any loss of energy due to deformation, heat, or sound.
Example:
The idealized collision between two perfectly bouncy superballs would be an elastic collision, with no energy lost as sound or heat.
Impulse
The effect of a force acting over a period of time, which results in a change in an object's momentum. It is equal to the force multiplied by the time interval ($\vec{J} = \vec{F}\Delta t$).
Example:
An airbag in a car increases the time over which the force of impact acts on a passenger, thereby reducing the magnitude of the force and the impulse felt by the person.
Impulse-Momentum Theorem
States that the impulse applied to an object is equal to the change in its momentum. This theorem links force and time to changes in motion.
Example:
According to the Impulse-Momentum Theorem, a baseball bat exerting a large force for a short time on a ball causes a significant change in the ball's momentum, sending it flying.
Inelastic Collisions
Collisions in which momentum is conserved, but kinetic energy is not. Some kinetic energy is transformed into other forms, such as heat, sound, or deformation.
Example:
When a car crashes into a tree and crumples, it's an inelastic collision because much of the kinetic energy is absorbed and converted into deformation and sound.
Kinetic Energy Conservation
The principle that the total kinetic energy of a system remains constant before and after an interaction, a characteristic specifically of elastic collisions.
Example:
In a theoretical scenario where two identical billiard balls collide head-on and bounce perfectly, their total kinetic energy conservation would mean no energy is lost to friction or sound.
Momentum
A vector quantity representing an object's 'oomph' in motion, calculated as the product of its mass and velocity ($\vec{p} = m\vec{v}$). Its direction is the same as the velocity.
Example:
A bowling ball rolling down the lane has significant momentum due to its large mass and speed, making it effective at knocking over pins.
Perfectly Inelastic Collision
A specific type of inelastic collision where the colliding objects stick together after impact and move as a single combined mass.
Example:
If a dart hits a target and embeds itself, it's a perfectly inelastic collision because the dart and target move together as one unit afterward.
Vector Quantity
A physical quantity that has both magnitude (size) and direction. Examples include velocity, force, and momentum.
Example:
When a soccer player kicks a ball, the force applied is a vector quantity because it has both a strength (magnitude) and a specific direction.