Glossary
1D Collision
A collision where all motion occurs along a single straight line, simplifying vector analysis as only direction (positive/negative) needs to be considered.
Example:
Two bumper cars colliding head-on along a straight path is an example of a 1D collision.
2D Collision
A collision where motion occurs in a plane, requiring vector components to be analyzed separately along two perpendicular axes.
Example:
A cue ball striking another billiard ball at an angle, causing both to scatter across the table, is a classic 2D collision.
Center-of-Mass Velocity
The velocity of the system's center of mass, which represents the average motion of the entire system of objects.
Example:
Even if a firework explodes into many pieces, the center-of-mass velocity of all the fragments combined continues along the same parabolic trajectory it had before the explosion.
Center-of-Mass Velocity (v_cm)
The velocity of the hypothetical point representing the average position of the total mass of a system.
Example:
If a rocket in deep space expels fuel, its center-of-mass velocity remains constant because no external forces are acting on the rocket-fuel system.
Conservation of Linear Momentum
A fundamental principle stating that the total momentum of an isolated system remains constant if no net external forces act on it.
Example:
When a firecracker explodes in mid-air, the total momentum of all its fragments combined remains the same as the momentum of the firecracker just before it exploded.
Conservation of Linear Momentum
A fundamental principle stating that the total linear momentum of an isolated system remains constant if no net external force acts upon it.
Example:
When a cannon fires a projectile, the conservation of linear momentum dictates that the cannon recoils backward as the projectile moves forward.
Elastic Collision
A type of collision where both momentum and kinetic energy are conserved.
Example:
The collision between two billiard balls is often approximated as an elastic collision, where kinetic energy is largely conserved.
Elastic Collision
A type of collision where both momentum and kinetic energy are conserved.
Example:
The idealized collision between two perfectly bouncy superballs, where no energy is lost to heat or sound, is an elastic collision.
External Force
A force originating from outside the defined system that can change the system's total momentum.
Example:
Air resistance acting on a falling object is an external force if the object itself is defined as the system.
External Forces
Forces originating from outside a defined system that can change the system's total momentum.
Example:
When a skater pushes off a wall, the force from the wall is an external force on the skater, changing their momentum.
Impulse
The change in momentum of an object, equal to the average net force acting on the object multiplied by the time interval over which the force acts.
Example:
A baseball bat exerts a large impulse on a ball over a short time, causing a significant change in the ball's momentum.
Impulse
A measure of the change in momentum of an object, calculated as the product of the average net force acting on an object and the time interval over which the force acts.
Example:
Hitting a golf ball with a club delivers a significant impulse, causing a large change in the ball's momentum.
Impulse-Momentum Theorem
A theorem stating that the change in an object's momentum is equal to the impulse applied to it.
Example:
A catcher's mitt moving backward when catching a fastball increases the time of impact, reducing the force on the hand, as explained by the Impulse-Momentum Theorem.
Inelastic Collision
A type of collision where momentum is conserved, but kinetic energy is not conserved, often due to deformation or heat generation.
Example:
When two clay balls collide and stick together, it's an inelastic collision because kinetic energy is lost as they deform and generate heat.
Inelastic Collision
A type of collision where momentum is conserved, but kinetic energy is not, as some kinetic energy is transformed into other forms like heat, sound, or deformation.
Example:
When a bullet embeds itself into a block of wood, it's an inelastic collision because kinetic energy is lost due to the deformation of the wood and the bullet.
Isolated System
A system where no net external forces act upon it, ensuring that the total momentum within its boundaries remains constant.
Example:
Two astronauts pushing off each other in deep space can be considered an isolated system for momentum analysis, as external forces like gravity are negligible.
Momentum
A vector quantity representing an object's 'oomph' or quantity of motion, calculated as the product of its mass and velocity.
Example:
A massive truck moving slowly can have more momentum than a small car moving quickly.
Newton's Third Law
States that for every action, there is an equal and opposite reaction, explaining why internal forces within a system do not change its total momentum.
Example:
When a swimmer pushes off the wall, the wall pushes back with an equal and opposite force, propelling the swimmer forward.
Newton's Third Law
States that for every action, there is an equal and opposite reaction, meaning that forces and impulses between interacting objects are equal in magnitude and opposite in direction.
Example:
When a swimmer pushes water backward, the water pushes the swimmer forward with an equal and opposite force, illustrating Newton's Third Law.
Sum of Momenta
The total momentum of a system, found by taking the vector sum of the individual momenta of all objects within that system.
Example:
Before a collision, the sum of momenta of two interacting objects must equal their sum of momenta after the collision in an isolated system.
System Boundaries
The imaginary line or conceptual division that separates the objects included in a physics problem from their surroundings.
Example:
When analyzing a car crash, defining the system as just the two cars allows you to see how their combined momentum is conserved if external forces like friction are negligible.
System Boundaries
The conceptual limits defining which objects are included within a system for analysis, which is crucial for determining if external forces are present.
Example:
When analyzing a car crash, carefully defining the system boundaries to include both vehicles allows for the application of momentum conservation principles.
Total System Momentum
The vector sum of the individual momenta of all objects within a defined system.
Example:
Before a bowling ball hits the pins, the total system momentum is the momentum of the ball itself, assuming the pins are initially at rest.