Foundation Physics: Complete Course

Physics Fundamentals & Units

Physics is the study of matter, energy, and their interactions. Everything in physics builds from fundamental quantities and mathematical relationships.

SI Base Units

Quantity	Unit	Symbol	Dimension
Length	meter	m	[L]
Mass	kilogram	kg	[M]
Time	second	s	[T]
Electric Current	ampere	A	[I]
Temperature	kelvin	K	[Θ]
Amount of Substance	mole	mol	[N]
Luminous Intensity	candela	cd	[J]

Derived Units & Dimensional Analysis

Common Derived Units

Velocity: m/s = [L][T]^(-1)
Acceleration: m/s² = [L][T]^(-2)
Force: N = kg⋅m/s² = [M][L][T]^(-2)
Energy: J = N⋅m = kg⋅m²/s² = [M][L]²[T]^(-2)
Power: W = J/s = [M][L]²[T]^(-3)

Scientific Notation & Significant Figures

Scientific Notation: Express large/small numbers as a × 10^n where 1 ≤ a < 10

Examples:

Speed of light: c = 3.00 × 10⁸ m/s
Planck's constant: h = 6.626 × 10^(-34) J⋅s
Electron mass: m_e = 9.109 × 10^(-31) kg

Dimensional Analysis Tip: Always check that your equation's dimensions match on both sides. This catches most algebra mistakes and helps verify formula correctness.

Kinematics: Motion Without Forces

Kinematics describes motion using position, velocity, and acceleration without considering the forces that cause motion.

Basic Kinematic Variables

Position, Velocity, and Acceleration

Position: x(t)
Velocity: v = dx/dt
Acceleration: a = dv/dt = d²x/dt²

x = position (m)
v = velocity (m/s)
a = acceleration (m/s²)
t = time (s)

Kinematic Equations (Constant Acceleration)

The Big Four Kinematic Equations

v = v₀ + at
x = x₀ + v₀t + ½at²
v² = v₀² + 2a(x - x₀)
x = x₀ + ½(v₀ + v)t

v₀ = initial velocity
v = final velocity
a = acceleration (constant)
x₀ = initial position
x = final position
t = time

Example: Free Fall Problem

Problem: A ball is dropped from a height of 45 meters. How long does it take to hit the ground?

Step 1: Identify known values
y₀ = 45 m, y = 0 m, v₀ = 0 m/s, a = -9.8 m/s²

Step 2: Choose appropriate equation
y = y₀ + v₀t + ½at²

Step 3: Substitute and solve
0 = 45 + 0 + ½(-9.8)t²
-45 = -4.9t²
t² = 45/4.9 = 9.18
t = 3.03 seconds

2D Projectile Motion

Projectile Motion Components

Horizontal: x = v₀ₓt = v₀cos(θ)t
Vertical: y = v₀ᵧt - ½gt² = v₀sin(θ)t - ½gt²
Range: R = (v₀²sin(2θ))/g
Max Height: H = (v₀²sin²(θ))/(2g)

v₀ = initial speed
θ = launch angle
g = 9.8 m/s² (gravitational acceleration)
R = horizontal range
H = maximum height

Dynamics: Forces and Newton's Laws

Dynamics explains why objects move by studying the forces acting on them. Newton's three laws form the foundation of classical mechanics.

Newton's First Law (Law of Inertia)

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

ΣF = 0 ⟹ a = 0

Newton's Second Law

The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.

ΣF = ma

ΣF = net force (N)
m = mass (kg)
a = acceleration (m/s²)

Newton's Third Law

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

F₁₂ = -F₂₁

Common Forces

Force Equations

Weight: W = mg
Normal Force: N (perpendicular to surface)
Friction: f = μN
Spring Force: F = -kx
Gravitational: F = G(m₁m₂)/r²

μ = coefficient of friction
k = spring constant (N/m)
x = displacement from equilibrium
G = 6.674 × 10^(-11) N⋅m²/kg²

Free Body Diagram Example:

↑ N (Normal Force)
← f [BLOCK] F →
↓ mg (Weight)

Net Force: ΣF = F - f = ma

Example: Inclined Plane

Problem: A 10 kg box slides down a 30° incline with μ = 0.2. Find the acceleration.

Step 1: Break weight into components
mg∥ = mg sin(30°) = 10 × 9.8 × 0.5 = 49 N (down incline)
mg⊥ = mg cos(30°) = 10 × 9.8 × 0.866 = 84.9 N (into incline)

Step 2: Find normal force
N = mg⊥ = 84.9 N

Step 3: Calculate friction
f = μN = 0.2 × 84.9 = 17.0 N (up incline)

Step 4: Apply Newton's 2nd Law
ΣF = mg∥ - f = 49 - 17 = 32 N
a = ΣF/m = 32/10 = 3.2 m/s²

Energy, Work, and Power

Energy is the capacity to do work. The conservation of energy is one of the most fundamental principles in physics.

Types of Energy

Mechanical Energy

Kinetic Energy: KE = ½mv²
Gravitational PE: PE = mgh
Elastic PE: PE = ½kx²
Total Mechanical Energy: E = KE + PE

m = mass (kg)
v = velocity (m/s)
h = height (m)
k = spring constant (N/m)
x = compression/extension (m)

Work and Power

Work-Energy Theorem

Work: W = F⋅d⋅cos(θ)
W = ΔKE = KE_final - KE_initial
Power: P = W/t = F⋅v
Efficiency: η = (Useful Energy Out)/(Total Energy In)

W = work done (J)
F = force (N)
d = displacement (m)
θ = angle between F and d
P = power (W = J/s)
η = efficiency (dimensionless)

Conservation of Energy

Energy cannot be created or destroyed, only transformed from one form to another.

E_initial = E_final

KE₁ + PE₁ = KE₂ + PE₂ (no friction)

Example: Pendulum Energy

Problem: A 2 kg pendulum swings from 1.5 m height. What's its speed at the bottom?

Step 1: Energy at top
KE₁ = 0 (starts from rest)
PE₁ = mgh = 2 × 9.8 × 1.5 = 29.4 J

Step 2: Energy at bottom
PE₂ = 0 (reference level)
KE₂ = ½mv² (unknown)

Step 3: Apply conservation
29.4 = ½ × 2 × v²
v² = 29.4
v = 5.42 m/s

Momentum and Collisions

Momentum describes the motion of objects and is always conserved in isolated systems, making it crucial for analyzing collisions.

Linear Momentum

Momentum and Impulse

Momentum: p = mv
Impulse: J = FΔt = Δp
Conservation: p_total_initial = p_total_final

p = momentum (kg⋅m/s)
m = mass (kg)
v = velocity (m/s)
J = impulse (N⋅s)
F = average force (N)
Δt = time interval (s)

Types of Collisions

Collision Analysis

Elastic: KE conserved + momentum conserved
v₁f = ((m₁-m₂)/(m₁+m₂))v₁ᵢ + ((2m₂)/(m₁+m₂))v₂ᵢ

Inelastic: Only momentum conserved
m₁v₁ᵢ + m₂v₂ᵢ = (m₁+m₂)v_f

Coefficient of Restitution: e = -(v₁f - v₂f)/(v₁ᵢ - v₂ᵢ)

e = 1 (perfectly elastic)
e = 0 (perfectly inelastic)
0 < e < 1 (real collisions)

Rotational Motion

Rotational motion involves objects spinning about an axis. The concepts parallel linear motion but use angular quantities.

Angular Kinematics

Rotational Equations

Angular Position: θ (radians)
Angular Velocity: ω = dθ/dt
Angular Acceleration: α = dω/dt
ω = ω₀ + αt
θ = θ₀ + ω₀t + ½αt²

θ = angular position (rad)
ω = angular velocity (rad/s)
α = angular acceleration (rad/s²)
1 revolution = 2π radians

Rotational Dynamics

Torque and Moment of Inertia

Torque: τ = rF sin(θ) = Iα
Moment of Inertia: I = Σmᵢrᵢ²
Rotational KE: KE_rot = ½Iω²
Angular Momentum: L = Iω

τ = torque (N⋅m)
r = distance from axis (m)
I = moment of inertia (kg⋅m²)
L = angular momentum (kg⋅m²/s)

Thermodynamics

Thermodynamics studies heat, temperature, and energy transfer. It bridges mechanics with statistical physics and chemistry.

Temperature and Heat

Temperature Scales

Celsius to Kelvin: K = °C + 273.15
Fahrenheit: °F = (9/5)°C + 32
Heat Transfer: Q = mcΔT
Heat Capacity: C = mc

Q = heat energy (J)
m = mass (kg)
c = specific heat capacity (J/kg⋅K)
ΔT = temperature change (K or °C)
C = heat capacity (J/K)

Laws of Thermodynamics

First Law of Thermodynamics

Energy is conserved: the change in internal energy equals heat added minus work done by the system.

ΔU = Q - W

ΔU = change in internal energy (J)
Q = heat added to system (J)
W = work done by system (J)

Second Law of Thermodynamics

Entropy of an isolated system always increases. Heat flows naturally from hot to cold.

ΔS ≥ 0 (isolated system)

Efficiency: η = 1 - T_cold/T_hot (Carnot limit)

Ideal Gas Law

Gas Properties

PV = nRT = NkT
Kinetic Theory: PV = (1/3)Nm⟨v²⟩
Average KE: ⟨KE⟩ = (3/2)kT

P = pressure (Pa)
V = volume (m³)
n = moles, N = number of molecules
R = 8.314 J/mol⋅K, k = 1.381 × 10^(-23) J/K
T = absolute temperature (K)

Waves and Sound

Waves transfer energy without transferring matter. Understanding wave properties is essential for sound, light, and quantum mechanics.

Wave Properties

Wave Equation

v = fλ
y(x,t) = A sin(kx - ωt + φ)
Wave number: k = 2π/λ
Angular frequency: ω = 2πf

v = wave speed (m/s)
f = frequency (Hz)
λ = wavelength (m)
A = amplitude (m)
k = wave number (rad/m)
ω = angular frequency (rad/s)
φ = phase constant (rad)

Sound Waves

Sound Properties

Speed in air: v = 343 m/s (at 20°C)
Intensity: I = P/A = (1/2)ρvω²A²
Sound Level: β = 10 log(I/I₀)
Doppler Effect: f' = f((v ± v_observer)/(v ± v_source))

I = intensity (W/m²)
I₀ = 10^(-12) W/m² (threshold of hearing)
β = sound level (dB)
ρ = air density (kg/m³)
+ when approaching, - when receding

Wave Interference:

Constructive: Waves add when in phase (path difference = nλ)
Destructive: Waves cancel when out of phase (path difference = (n+½)λ)
Standing Waves: Form when waves reflect and interfere with themselves

Electricity and Electric Fields

Electric phenomena arise from electric charges and their interactions. Understanding electricity is fundamental to modern technology.

Electric Force and Field

Coulomb's Law and Electric Field

Electric Force: F = k(q₁q₂)/r²
Electric Field: E = F/q = kQ/r²
Field of Point Charge: E = kq/r²
Force on Charge in Field: F = qE

k = 8.99 × 10⁹ N⋅m²/C² (Coulomb's constant)
q = electric charge (C)
r = distance (m)
E = electric field strength (N/C)

Electric Potential

Potential Energy and Voltage

Electric PE: U = kq₁q₂/r
Electric Potential: V = U/q = kQ/r
Potential Difference: ΔV = W/q
Relation to Field: E = -dV/dr

U = electric potential energy (J)
V = electric potential (V = J/C)
ΔV = voltage (V)
Work moves charge against field

Electric Circuits

Circuit Analysis

Ohm's Law: V = IR
Power: P = IV = I²R = V²/R
Series: R_total = R₁ + R₂ + R₃...
Parallel: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃...

V = voltage (V)
I = current (A)
R = resistance (Ω)
P = power (W)

Circuit Diagram Symbols:

Battery: ——|+|—————|—|——
Resistor: ————/\/\/\————
Current: ————————→————————

Kirchhoff's Laws:
∑I_in = ∑I_out (current law)
∑V = 0 (voltage law around loop)

Magnetism and Electromagnetic Induction

Moving electric charges create magnetic fields, and changing magnetic fields create electric fields. This relationship underlies all electromagnetic phenomena.

Magnetic Force

Magnetic Force Laws

Force on Moving Charge: F = qvB sin(θ)
Force on Current: F = ILB sin(θ)
Magnetic Field of Wire: B = (μ₀I)/(2πr)
Force Between Wires: F/L = (μ₀I₁I₂)/(2πr)

B = magnetic field (T = Tesla)
μ₀ = 4π × 10^(-7) T⋅m/A
θ = angle between v and B
L = length of conductor (m)

Electromagnetic Induction

Faraday's and Lenz's Laws

Magnetic Flux: Φ = BA cos(θ)
Faraday's Law: ε = -dΦ/dt
Motional EMF: ε = BLv
Self-Inductance: ε = -L(dI/dt)

Φ = magnetic flux (Wb = Weber)
ε = induced EMF (V)
L = inductance (H = Henry)
Lenz's Law: induced current opposes change

Light and Optics

Light exhibits both wave and particle properties. Geometric optics describes light rays, while wave optics explains interference and diffraction.

Geometric Optics

Reflection and Refraction

Law of Reflection: θᵢ = θᵣ
Snell's Law: n₁ sin(θ₁) = n₂ sin(θ₂)
Critical Angle: sin(θc) = n₂/n₁
Mirror Equation: 1/f = 1/dₒ + 1/dᵢ

θᵢ = incident angle
θᵣ = reflected angle
n = index of refraction
f = focal length
dₒ = object distance
dᵢ = image distance

Lens Optics

Thin Lens Equation

Lens Equation: 1/f = 1/dₒ + 1/dᵢ
Magnification: m = -dᵢ/dₒ = hᵢ/hₒ
Lens Maker's Equation: 1/f = (n-1)(1/R₁ - 1/R₂)
Power: P = 1/f (diopters)

m = magnification (dimensionless)
h = height
R = radius of curvature
Positive f = converging lens
Negative f = diverging lens

Wave Optics

Interference and Diffraction

Double Slit: d sin(θ) = mλ (bright fringes)
Single Slit: a sin(θ) = mλ (dark fringes)
Grating: d sin(θ) = mλ
Resolution: θ = 1.22λ/D (Rayleigh criterion)

d = slit separation
a = slit width
m = order (0, ±1, ±2...)
D = aperture diameter
λ = wavelength

Modern Physics Introduction

Modern physics emerged in the early 1900s with relativity and quantum mechanics, revealing the strange behavior of very fast, very small, or very massive objects.

Special Relativity

Einstein's Relativity

Time Dilation: Δt = γΔt₀
Length Contraction: L = L₀/γ
Lorentz Factor: γ = 1/√(1 - v²/c²)
Mass-Energy: E = mc²
Total Energy: E² = (pc)² + (mc²)²

c = 3.00 × 10⁸ m/s (speed of light)
γ = Lorentz factor
Δt₀ = proper time
L₀ = proper length
p = relativistic momentum

Quantum Mechanics Basics

Quantum Foundations

Planck's Equation: E = hf
de Broglie Wavelength: λ = h/p
Photoelectric Effect: hf = φ + KE_max
Uncertainty Principle: ΔxΔp ≥ ℏ/2

h = 6.626 × 10^(-34) J⋅s (Planck's constant)
ℏ = h/(2π) (reduced Planck's constant)
φ = work function (J)
Δx = position uncertainty
Δp = momentum uncertainty

Atomic Physics

Atomic Structure

Bohr Model: rₙ = n²(ℏ²/mke²)
Energy Levels: Eₙ = -13.6 eV/n²
Photon Emission: hf = E_initial - E_final
Binding Energy: BE = (Z⋅m_H + N⋅m_n - M_atom)c²

n = principal quantum number
m = electron mass
k = Coulomb's constant
e = elementary charge
Z = atomic number, N = neutron number

Problem-Solving Strategy

Universal Physics Problem-Solving Method

Understand: Read carefully, identify what's given and what's asked
Visualize: Draw diagrams, free body diagrams, or circuit diagrams
Plan: Choose relevant principles and equations
Execute: Apply mathematics carefully, track units
Check: Verify units, magnitude, and physical reasonableness

Always start with fundamentals! Most complex problems can be solved using basic principles like F=ma, conservation of energy, or conservation of momentum.

Common Mistakes: Forgetting to convert units, using wrong sign conventions, not drawing proper diagrams, confusing scalar and vector quantities, mixing up formulas from different topics.

Quick Reference Calculator

Use these for quick conversions and checks:

Physics Glossary

Acceleration

Rate of change of velocity; a = dv/dt. Measured in m/s².

Angular Momentum

Rotational analog of linear momentum; L = Iω. Conserved in absence of external torques.

Electric Field

Force per unit charge; E = F/q. Describes the electric force environment around charges.

Energy

Capacity to do work. Comes in many forms: kinetic, potential, thermal, electromagnetic, etc.

Entropy

Measure of disorder in a system. Always increases in isolated systems (2nd Law of Thermodynamics).

Force

Push or pull that can change an object's motion; F = ma. Measured in Newtons (N).

Frequency

Number of oscillations per second; f = 1/T. Measured in Hertz (Hz).

Inertia

Tendency of objects to resist changes in motion. Related to mass in Newton's 1st Law.

Interference

Superposition of waves resulting in amplification (constructive) or cancellation (destructive).

Momentum

Quantity of motion; p = mv. Conserved in isolated systems.

Power

Rate of energy transfer; P = W/t = dE/dt. Measured in Watts (W).

Potential Energy

Stored energy due to position or configuration. Can be gravitational, elastic, electric, etc.

Quantum

Discrete packet of energy; E = hf. Energy comes in quantized amounts, not continuous.

Torque

Rotational force; τ = rF sin(θ). Causes angular acceleration.

Vector

Quantity with both magnitude and direction (velocity, force, field). Distinguished from scalars.

Wavelength

Distance between adjacent peaks in a wave; λ = v/f. Fundamental wave property.

Work

Energy transfer when force acts through distance; W = F⋅d⋅cos(θ). Measured in Joules (J).

Physics in the Real World

Applications You Use Daily

Smartphones: Semiconductors (quantum mechanics), touchscreens (capacitance), GPS (relativity), cameras (optics), speakers (waves)

Transportation: Internal combustion engines (thermodynamics), electric vehicles (electromagnetic induction), aerodynamics (fluid mechanics)

Medicine: X-rays (electromagnetic radiation), MRI (nuclear magnetic resonance), ultrasound (wave physics), laser surgery (optics)

Energy: Solar panels (photoelectric effect), nuclear power (mass-energy equivalence), wind turbines (rotational mechanics)

Study Strategy: Physics concepts build on each other. Master the math behind each concept, practice lots of problems, and always connect new ideas to what you already know. Draw pictures for everything!

Math Prerequisites: You'll need algebra, trigonometry, and basic calculus. Don't skip the math - physics IS applied mathematics describing the natural world.

Foundation Physics

Physics Course Modules

Physics Fundamentals & Units

SI Base Units

Derived Units & Dimensional Analysis

Scientific Notation & Significant Figures

Kinematics: Motion Without Forces

Basic Kinematic Variables

Kinematic Equations (Constant Acceleration)

2D Projectile Motion

Dynamics: Forces and Newton's Laws

Common Forces

Energy, Work, and Power

Types of Energy

Work and Power

Momentum and Collisions

Linear Momentum

Types of Collisions

Rotational Motion

Angular Kinematics

Rotational Dynamics

Thermodynamics

Temperature and Heat

Laws of Thermodynamics

Ideal Gas Law

Waves and Sound

Wave Properties

Sound Waves

Electricity and Electric Fields

Electric Force and Field

Electric Potential

Electric Circuits

Magnetism and Electromagnetic Induction

Magnetic Force

Electromagnetic Induction

Light and Optics

Geometric Optics

Lens Optics

Wave Optics

Modern Physics Introduction

Special Relativity

Quantum Mechanics Basics

Atomic Physics

Problem-Solving Strategy

Universal Physics Problem-Solving Method

Quick Reference Calculator

Physics Glossary

Physics in the Real World

Applications You Use Daily