Physics Final

Scalar vs. Vector

A scalar has only magnitude (just a number, like speed), while a vector has both magnitude and direction (like velocity).

Distance vs. Displacement

Distance is a scalar measuring total ground covered. Displacement is a vector measuring how far you are from where you started, relative to your initial position.

Speed vs. Velocity

Speed is a scalar tracking the rate of covering distance. Velocity is a vector tracking the rate at which position changes.

Acceleration

A vector measuring the rate of change of velocity over time.

Freefall

The state of an object moving solely under the influence of the gravitational force.

Direction of Gravitational Acceleration

Always points straight down toward the surface, regardless of whether the object is moving up, down, or is at the absolute peak of its path.

Velocity at Peak Flight Path

The vertical component of velocity is exactly zero at the highest point of travel.

Displacement vs. Time Graph Slope

The slope of the line is equal to the velocity of the object.

Displacement vs. Time Graph Signs

A positive slope indicates moving forward or up, while a negative slope indicates moving backward or down.

Velocity vs. Time Graph Slope

The slope of the line is equal to the acceleration of the object.

Velocity vs. Time Graph Area Under Curve

The total area under the curve is equal to the displacement of the object.

Acceleration vs. Time Graph Area Under Curve

The total area under the curve is equal to the change in velocity of the object.

Core Strategy for Two-Dimensional Projectile Motion

Break the problem completely down into two completely independent one-dimensional problems: horizontal and vertical.

Recombining Two-Dimensional Components

Components are brought back together using basic right-triangle trigonometric functions and the Pythagorean Theorem.

Horizontal Acceleration of a Projectile

Acceleration in the horizontal direction is zero, meaning horizontal velocity remains completely constant throughout the entire flight.

Initial Vertical Velocity of a Horizontal Launch

The initial vertical component of velocity is exactly zero when launched perfectly flat.

Peak Symmetrical Launch Condition

For a projectile launched and landed at the same height, the peak height occurs exactly halfway through the total horizontal range.

Relative Motion Vectors

Choose a stationary reference frame, break vectors into components, add the components, and recombine them using trigonometry.

Inertia

An object's natural resistance to a change in its state of motion, measured quantitatively by its mass.

Newton's First Law of Motion

An object at rest stays at rest, and an object in motion stays in motion with constant velocity, unless acted upon by an external net force.

Newton's Second Law of Motion

Net force equals mass times acceleration, meaning acceleration is directly proportional to net force and inversely proportional to mass.

Newton's Third Law of Motion

For every action force, there is an equal and opposite reaction force.

SI Unit of Force

The Newton, which expands to baseline units of kilograms times meters per second squared.

Resistive Force

A force that always acts in the direction directly opposite to the object's relative motion.

Friction Concept

Friction depends on the roughness of the surfaces and how tightly the objects are pressed together by the normal force.

Normal Force

The supporting force exerted by a surface on an object resting against it, always pointing perpendicular to that contact surface.

Coefficient of Friction Determination

A unitless value that depends strictly on the specific molecular materials of the two surfaces in contact.

Static vs. Kinetic Friction Coefficients

The static coefficient is always larger than the kinetic coefficient, meaning it takes more force to break surface bonds from rest than to keep them sliding.

Essential Step for Force Problems

Draw a complete Free Body Diagram to isolate the object and sum the forces along each coordinate direction.

Incline Plane Coordinate Adjustment

Rotate the coordinate framework so the main axis runs parallel to the incline surface and the secondary axis runs perpendicular to it.

Multi-Body Pulley Coordinate Setup

Bend the directional axis around the pulley, following the straight line of the connecting string.

Uniform Circular Motion

An object moving in a circular trajectory path at a completely constant speed.

Period vs. Frequency

Period is the time required per cycle. Frequency is the number of cycles completed per unit of time. They are mathematical inverses.

Centripetal Acceleration Behavior

Points directly toward the center of the circular path, changing the object's direction but not its linear speed.

Linear Orbital Speed from Period

Calculated by dividing the total circular circumference path by the time required for one full cycle.

Kepler's First Law

All orbiting objects travel in elliptical paths with the central body located at one of the two internal foci.

Kepler's Second Law

An orbiting object sweeps out equal areas of its ellipse in equal time intervals, meaning it travels faster when it is closer to the central mass.

Kepler's Third Law

For objects orbiting the same central mass, the square of the orbital period is directly proportional to the cube of the orbital distance.

Newton's Law of Universal Gravitation Relationship

Every object attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Distance Measurement for Gravity

Distance must always be measured strictly from the absolute center of mass of the two interacting objects.

Energy

Defined fundamentally as the physical ability of a system to perform work.

Gravitational Potential Energy Factors

Depends on the mass of the object, the strength of the local gravitational field, and its relative height above a baseline surface.

Kinetic Energy Factors

Depends on the mass of the object and the square of its current linear speed.

Work Concept

Exerting a force over a displacement distance, which transfers energy into or out of a system.

Effective Force Component for Work

Only the components of the force that act parallel to the directional displacement vector do work.

Work-Energy Theorem

The net work done on an object by all forces combined equals its total change in kinetic energy.

Power

The temporal rate of doing work or the rate at which energy is transferred over time.

Conservative Force

A force that is path-independent where the work done depends only on the initial and final states of the object.

Non-Conservative Force

A force that is path-dependent where mechanical energy is actively converted into non-mechanical forms like heat or sound.

Conservation of Total Mechanical Energy

Total mechanical energy remains constant when there are exclusively conservative forces acting on a closed system.

Non-Conservative Work Relation

The work done by non-conservative forces equals the net change in the total mechanical energy of the system.

Simple Harmonic Motion

An ongoing, repetitive oscillation between two geometric endpoints without any net loss of mechanical energy.

Restoring Force

A force that always points directly back toward the system's central equilibrium position.

Hooke's Law Concept

The force exerted by a spring is directly proportional to its displacement distance and always opposes the direction of the stretch or compression.

Spring Constant Meaning

A value representing the baseline structural stiffness or rigidity of a specific spring.

Period of a Mass-Spring System Dependency

The time for one full oscillation depends directly on the hanging mass and inversely on the stiffness of the spring.

Period of a Simple Pendulum Dependency

The time for one full swing depends directly on the length of the string and inversely on the local acceleration of gravity, completely independent of mass.

Torque

A rotational force effect that changes an object's angular or rotational motion.

Effective Force Component for Torque

Only the components of a force acting perpendicular to the lever arm generate torque.

Torque Sign Conventions

Clockwise rotations are traditionally treated as negative, and counter-clockwise rotations are treated as positive.

Static Equilibrium Conditions

Two simultaneous conditions are required: the net external force must equal zero, and the net external torque must equal zero.

Linear Momentum

A vector quantity tracking mass in motion, pointing in the exact same direction as the object's velocity vector.

Impulse-Momentum Theorem

The average force applied multiplied by the contact time equals the object's total change in momentum.

Conservation of Linear Momentum

Total momentum remains constant in an isolated system containing no net external forces.

Two-Dimensional Momentum Conservation

You must balance and conserve momentum independently along both the horizontal axis and the vertical axis.

Elastic Collision

Objects bounce off cleanly where both total momentum and total kinetic energy are conserved.

Inelastic Collision

Objects stick together or deform where total momentum is conserved, but a portion of kinetic energy is lost to internal heat or deformation.

Law of Conservation of Charge

Charge is an intrinsic property of matter that cannot be created or destroyed; it can only be transferred from one object to another.

Conductor

A material containing loose or free electrons that allow electrical charges to move freely across its structure.

Insulator

A material whose electrons are tightly bound to their atoms, preventing free charge movement.

Semiconductor

A material that normally behaves as an insulator but can allow limited charge movement under specific physical conditions.

Charging by Conduction

Direct physical contact transfers charge, leaving both interacting objects with the exact same type of net charge.

Charging by Induction

Rearranging charges inside an object near a ground path connection, leaving the target object with the opposite net charge without direct contact.

Coulomb's Law Relationship

The electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Electric Field Properties

A vector quantity that represents the force per unit charge, pointing away from positive source charges and towards negative source charges.

Electric Field Diagram Spacing

Lines packed tightly close together indicate a structurally stronger electric field region.

Electrostatic Field Inside a Conductor

The net electric field inside a perfect conductor in electrostatic equilibrium is exactly zero.

Millikan's Oil Drop Experiment

A landmark experiment that measured the fundamental elementary charge of an individual electron.

Electric Potential vs. Electric Potential Energy

Electric potential is a scalar quantity tracking the potential energy per unit of charge at a specific location.

Equipotential Line Geometry

Equipotential lines represent locations of equal voltage and always cross perpendicular to electric field lines.

Electric Current

The rate at which physical electrical charge passes through a specific cross-sectional point over time.

Wire Resistance Factors

Resistance increases with wire length and material resistivity, and decreases with an increase in cross-sectional area.

Ohm's Law Relationship

Current through a conductor is directly proportional to the voltage drop across it and inversely proportional to its resistance.

Electrical Power Concept

The rate at which electrical energy is converted into another form, depending on current, voltage, or resistance.

Resistors in Series Rule

They share the exact same current, but split the total voltage drop based on individual resistances.

Resistors in Parallel Rule

They share the exact same voltage drop, but split the total current across their parallel branches.

Equivalent Capacitance Trends

Capacitors add together directly when placed in parallel, but their inverses add together when placed in a series alignment.

Capacitor Charging Dynamics

Immediately after closing a switch, current starts at its maximum value and drops exponentially to zero, while voltage starts at zero and rises exponentially to its maximum.

Circuit Time Constant Meaning

The characteristic time required for a capacitor to charge or discharge a substantial percentage of its maximum capacity through a resistor.

Magnetic Field Creation

Magnetic fields are generated exclusively by moving charges or active electrical currents.

Magnetic Monopoles

Magnetic monopoles do not exist in classical physics; magnetic poles always occur as a pair containing both a North and South pole.

Magnetic Field Line Directions

Lines point out of the North pole and curve into the South pole outside of a permanent magnet.

Three-Dimensional Vector Field Notations

An X notation represents a vector pointing directly into the page; a dot notation represents a vector pointing directly out of the page.

Magnetic Force on a Moving Charge Condition

A charge experiences a magnetic force only if it is moving, and its velocity vector is not parallel to the magnetic field lines.

Work Done by a Magnetic Field

Zero work is performed because the magnetic force is always perpendicular to the velocity vector, altering path direction but never changing speed.

Magnetic Force on a Current-Carrying Wire

The force is directly proportional to the current, the length of the wire inside the field, the magnetic field strength, and the angle between them.

Parallel Current Wire Forces

Wires carrying parallel currents in the same direction attract each other; wires with currents running in opposite directions repel each other.

Magnetic Flux

The total measure of the magnetic field lines passing through a given cross-sectional area.

Faraday's Law of Induction

A time-varying change in magnetic flux passing through a loop of wire induces an electromotive force or voltage in that circuit.

Lenz's Law

The direction of an induced current always creates a secondary magnetic field that directly opposes the initial change in magnetic flux that created it.