Section 1: Forces, Motion, and Momentum

Collision

An event where two or more objects come into contact and exert forces on each other.

Kinetic Energy (KE)

The energy an object has due to its motion, calculated as 𝐾𝐸=1/2𝑚𝑣^2

Momentum (p)

The product of an object’s mass and velocity; a measure of how hard it is to stop the object.

Elastic Collision

A collision in which both momentum and kinetic energy are conserved; objects bounce off each other.

Ex. Two marbles colliding on a smooth surface and bouncing apart without losing energy.

Inelastic Collision

A collision in which momentum is conserved but kinetic energy is not; some energy is converted to heat, sound, or deformation.

Ex. A hockey puck hitting a goalie’s glove and stopping; momentum is conserved but some kinetic energy is lost.

Perfectly Inelastic Collision

A special case of an inelastic collision where the colliding objects stick together after impact.

Ex. Two blocks colliding and sticking together on a frictionless surface.

Momentum in Collisions

Total momentum of the system is conserved in all types of collisions.

Kinetic Energy in Collisions

Conserved only in elastic collisions; partially lost in inelastic collisions.

Total Momentum

The sum of the momenta of all objects in a system before and after a collision; remains constant in isolated systems.

Impulse

The change in momentum caused by a force applied over a period of time.

𝐽=𝐹Δ𝑡

Average Force (F)

The net force applied to an object over a time interval.

Time Interval (Δt)

The length of time during which a force acts on an object.

Impulse–Momentum Theorem

The impulse applied to an object equals its change in momentum.

Change in Momentum (Δp)

The difference between an object’s final momentum and initial momentum.

Longer Contact Time

Results in a smaller average force for the same impulse.

Shorter Contact Time

Results in a larger average force for the same impulse.

Impulse as a Vector Quantity

Impulse has both magnitude and direction, matching the direction of the applied force.

Impulse in Collisions

Determines how much an object’s momentum changes during an impact.

Momentum Formula

Momentum equals mass times velocity: p=m⋅v.

Units of Momentum

Kilogram meters per second (kg·m/s).

Mass (m)

The amount of matter in an object; measured in kilograms.

Velocity (v)

The speed of an object in a given direction; measured in meters per second.

Mass and Momentum

As mass increases, momentum increases if velocity stays the same.

Relationship between…

Relationship Between Velocity and Momentum

As velocity increases, momentum increases if mass stays the same.

High Momentum

Objects that are very massive, moving very fast, or both.

Low Momentum

Objects that are light, slow-moving, or both.

Changing Momentum

Momentum changes when an object’s velocity changes due to a force.

Force and Momentum Equation

Net force equals change in momentum divided by time: 𝐹=Δ𝑝/Δ𝑡

Stopping an Object

Requires removing all of its momentum using external forces.

Impulse

The effect of a force acting over a period of time that changes momentum (related to Δp).

Acceleration and Momentum

Acceleration is a change in velocity, which also means a change in momentum.

Vector Quantity

A quantity that has both magnitude and direction (momentum is a vector).

Law of Conservation of Momentum

In an isolated system, the total momentum remains constant.

Isolated System

A system where no external forces act and no mass enters or leaves.

Total Momentum

The sum of the momenta of all objects in a system.

Collision

An interaction where objects exert forces on each other, changing individual momenta.

Momentum Transfer

When one object loses momentum and another gains the same amount.

Frictionless Surface

An ideal surface with no external forces, allowing momentum to be conserved.

External Forces

Forces from outside a system that can change total momentum.

Why Momentum Is Useful

It helps analyze collisions and interactions without needing to track complex forces.

Atom

The basic building block of matter, made of a nucleus surrounded by electrons.

Nucleus

The dense center of an atom that contains protons and neutrons and most of the atom’s mass.

Proton

A positively charged particle found in the atomic nucleus.

Neutron

A neutral particle found in the atomic nucleus with no electric charge.

Electron

A negatively charged particle that exists in energy levels around the nucleus.

Electron Shells (Energy Levels)

Regions around the nucleus where electrons are likely to be found.

Electrostatic Repulsion

The force that causes positively charged protons to repel each other.

Nuclear Forces

Forces that act inside the atomic nucleus to hold protons and neutrons together.

Strong Nuclear Force

The strongest of the four fundamental forces; binds quarks together and holds protons and neutrons in the nucleus.

Purpose of the Strong Nuclear Force

Prevents the nucleus from flying apart due to electrostatic repulsion between protons.

Range of the Strong Nuclear Force

Extremely short; only works at very small (nuclear) distances.

Quarks

Fundamental particles that make up protons and neutrons.

Up Quark

A type of quark found in protons and neutrons.

Down Quark

A type of quark found in protons and neutrons.

Proton Quark Composition

Two up quarks and one down quark.

Neutron Quark Composition

Two down quarks and one up quark.

Gluons

Particles that carry the strong nuclear force and “glue” quarks together.

Weak Nuclear Force

A fundamental force responsible for radioactive decay and particle transformations.

Purpose of the Weak Nuclear Force

Allows quarks to change type, such as turning a proton into a neutron.

Radioactive Decay

A process in which unstable atoms release energy or particles due to the weak nuclear force.

Element Transformation

When an atom changes into a different element due to particle changes caused by the weak force.

Relative Strength of Forces

Strong nuclear force > electromagnetic force > weak nuclear force > gravitational force.

Why We Don’t Feel Nuclear Forces

They act only at extremely short distances inside atoms.

Nuclear Fusion

A process where light atomic nuclei combine to form a heavier nucleus, releasing large amounts of energy.

Fusion in Stars

Occurs when the strong nuclear force overcomes electromagnetic repulsion between nuclei.

Role of Gravity in Star Formation

Pulls gas and dust together to form a dense core.

Role of Electromagnetic Force in Stars

Helps atoms form and electrons stay bound to nuclei.

Role of Strong Nuclear Force in Stars

Allows nuclei to fuse, releasing energy that makes stars shine.

Role of Weak Nuclear Force in Stars

Enables particle changes that keep fusion reactions going.

Four Fundamental Forces

Gravitational force, electromagnetic force, strong nuclear force, and weak nuclear force.

Why Stars Shine

Energy released from nuclear fusion powered by the strong and weak nuclear forces.

Electromagnetic Force

The force that acts between charged particles; includes both electric and magnetic effects.

Why Electromagnetic Force Matters

It explains interactions between small objects where gravity is too weak to have a noticeable effect.

Electric Charge

A property of matter that can be positive or negative and causes electromagnetic interactions.

Point Charge

An electric charge treated as if all its charge is concentrated at a single point with no physical size.

Coulomb’s Law

An equation that describes the electrostatic force between two charged objects based on charge and distance.

Electrostatic Force (F)

The force of attraction or repulsion between two electric charges, measured in newtons.

Coulomb’s Constant (k)

A physical constant used in Coulomb’s law that determines the strength of the electrostatic force.

Charge Magnitude (q)

The amount of electric charge on an object, measured in coulombs (C).

Distance (r)

The separation between two charges, measured between their centers.

Like Charges Repel

Two charges with the same sign (both positive or both negative) push away from each other.

Opposite Charges Attract

A positive charge and a negative charge pull toward each other.

Direction of Electromagnetic Force

Depends on the signs of the charges; repulsive for like charges and attractive for opposite charges.

Direct Relationship (Charge)

Increasing the magnitude of either charge increases the electromagnetic force.

Inverse Square Relationship (Distance)

Increasing the distance between charges decreases the force by the square of the distance.

Inverse Square Law

Doubling the distance between charges reduces the electromagnetic force to one-fourth its original value.

Comparison to Gravity

Electromagnetic force is much stronger than gravitational force for small, charged objects.

Electric Field

A region around a charged object where other charges experience an electric force.

Magnetic Field

A region around moving charges or magnets where magnetic forces act.

Electromagnetism

The connection between electricity and magnetism as different aspects of the same force.

Michael Faraday

Scientist who discovered that changing magnetic fields can create electric currents.

Electromagnetic Induction

The process by which a changing magnetic field produces an electric current in a conductor.

Faraday’s Law

States that a changing magnetic field induces an electric current.

Changing Magnetic Field

A requirement for inducing current; a constant magnetic field does not produce current.

Induced Current

Electric current created by a changing magnetic field.

Heinrich Lenz

Scientist who explained the direction of induced current.

Lenz’s Law

The induced current always opposes the change in magnetic field that created it.

Opposition to Change

Induced currents resist increases or decreases in magnetic fields.

Alternating Current (AC)

Electric current that repeatedly changes direction, often produced by changing magnetic fields.

Coil and Magnet Interaction

Moving a magnet near a coil changes the magnetic field and induces current.