Glossary
Changing Momentum
A change in an object's momentum, which occurs when its velocity (either speed or direction) changes due to an impulse or net force.
Example:
When a soccer player kicks a stationary ball, the ball experiences a changing momentum from zero to a significant value.
Closed System
A system where no external forces act on the objects within it, meaning the total momentum of the system is conserved.
Example:
Two ice skaters pushing off each other on a frictionless rink can be considered a closed system because external forces like friction are negligible.
Collisions
Events where two or more objects exert large forces on each other over a short period, resulting in a change in their individual momenta.
Example:
A car crash is a classic example of collisions where momentum is conserved for the system of cars, even if the cars deform.
Collisions
Brief, intense interactions between objects where significant forces are exchanged over a short time interval.
Example:
When two billiard balls strike each other, they undergo a collision, transferring momentum and energy.
Conservation of Momentum
A fundamental principle stating that in an isolated system, the total linear momentum before an interaction (like a collision or explosion) is equal to the total linear momentum after the interaction.
Example:
In a perfectly isolated system, if a rocket expels gas backward, the rocket moves forward, demonstrating the conservation of momentum for the rocket-gas system.
Conservation of Momentum
A fundamental principle stating that in a closed system (one with no external forces), the total linear momentum remains constant before and after an interaction.
Example:
When a rocket expels exhaust gases, the conservation of momentum explains why the rocket moves forward; the backward momentum of the gases is balanced by the forward momentum of the rocket.
Elastic Collisions
A type of collision where both linear momentum and kinetic energy are conserved. Objects bounce off each other without any loss of kinetic energy to other forms.
Example:
The idealized bouncing of two perfectly hard billiard balls can be approximated as an elastic collision.
Elastic Collisions
Collisions in which both linear momentum and kinetic energy are conserved, and objects bounce off each other without deformation or energy loss to heat/sound.
Example:
The idealized collision between two perfectly bouncy superballs is an elastic collision, where kinetic energy is fully preserved.
Explosions
Events where internal forces cause a single object or system to break apart into multiple pieces, with the total momentum of the system remaining conserved.
Example:
When a firework shell bursts into many smaller pieces, the total momentum of all the fragments combined is conserved, illustrating an explosion.
Explosions
Events involving internal forces pushing objects apart, resulting in a change in momentum for the separated parts.
Example:
A firework bursting in the sky is an explosion, where internal forces propel fragments outward in various directions.
Impulse
The change in momentum of an object, also defined as the net force acting on an object multiplied by the time interval over which the force acts.
Example:
A soccer player kicking a ball applies an impulse to it, causing a rapid change in the ball's momentum.
Impulse-Momentum Theorem
A fundamental theorem stating that the impulse applied to an object is equal to the change in its linear momentum.
Example:
Using the Impulse-Momentum Theorem, engineers can design car crumple zones to increase the impact time, thereby reducing the force experienced by passengers during a collision.
Inelastic Collisions
A type of collision where linear momentum is conserved, but kinetic energy is not. Some kinetic energy is typically lost to heat, sound, or deformation.
Example:
When a dart sticks to a dartboard, it's an inelastic collision because kinetic energy is lost as the dart embeds itself.
Inelastic Collisions
Collisions in which linear momentum is conserved, but kinetic energy is not conserved, often due to energy conversion into heat, sound, or deformation.
Example:
A car crash where the vehicles crumple and deform is an inelastic collision, as much of the initial kinetic energy is converted into other forms.
Isolated System
A system where no net external forces act on the objects within it. This condition is crucial for the conservation of momentum to apply.
Example:
Two astronauts pushing off each other in deep space form an isolated system because there are no significant external forces like gravity or air resistance.
Kinetic Energy
The energy an object possesses due to its motion, calculated as $1/2 mv^2$. In collisions, it may or may not be conserved.
Example:
A runner sprinting has significant kinetic energy, which increases with both their mass and the square of their speed.
Linear Momentum
A measure of an object's motion, combining its mass and velocity. It represents the 'oomph' or 'push' an object has.
Example:
A bowling ball rolling down the lane has significant linear momentum due to its large mass and speed.
Linear Momentum
A vector quantity representing the 'oomph' an object has in its motion, calculated as the product of an object's mass and its velocity.
Example:
A bowling ball rolling down the lane has significant linear momentum due to its large mass and moderate speed.
Momentum Formula
The mathematical expression $\vec{p} = m\vec{v}$, where $\vec{p}$ is momentum, $m$ is mass, and $\vec{v}$ is velocity. It quantifies an object's momentum.
Example:
To calculate the momentum formula for a 0.15 kg baseball thrown at 40 m/s, you'd multiply its mass by its velocity.
Negative Momentum
Momentum assigned a negative value, typically indicating motion in the opposite direction of the chosen positive direction (e.g., left or downwards).
Example:
Following the same convention, if the skateboarder turns around and moves left, they now have negative momentum.
Object Model
A simplification strategy in physics where the complex internal forces and exact details of an interaction are ignored, focusing only on the initial and final states of the interacting objects.
Example:
When analyzing a car crash, physicists often use the object model to determine the vehicles' velocities before and after impact without detailing the crumpling process.
Perfectly Inelastic Collisions
A specific type of inelastic collision where the colliding objects stick together after impact, moving as a single combined mass.
Example:
When a bullet embeds itself into a block of wood, it's a perfectly inelastic collision because the two objects move together as one after the impact.
Positive Momentum
Momentum assigned a positive value, typically indicating motion in a chosen positive direction (e.g., right or upwards).
Example:
If we define right as positive, a skateboarder moving to the right has positive momentum.
Vector
A physical quantity that has both magnitude (size) and direction.
Example:
When describing the velocity of a car, you must state both its speed (e.g., 60 mph) and its direction (e.g., north), making velocity a vector.
Vector Addition (Momentum)
The process of combining multiple momentum vectors to find the net or total momentum of a system, considering both their magnitudes and directions.
Example:
When two billiard balls collide at an angle, you use vector addition to find the total momentum of the system before and after impact.
Vector Nature of Momentum
Momentum is a vector quantity, meaning it has both magnitude (size) and direction. Its direction is always the same as the object's velocity.
Example:
When a car drives north, its vector nature of momentum means its momentum also points north, not just that it has a certain amount of 'oomph'.