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Foundation Physics: Complete Course
Foundation Physics: Complete Course
Foundation Physics
Complete Course: From Basic Concepts to Modern Physics
Physics Course Modules
Fundamentals & Units
Kinematics
Dynamics & Forces
Energy & Work
Momentum
Rotational Motion
Thermodynamics
Waves & Sound
Electricity
Magnetism
Light & Optics
Modern Physics
Glossary
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.…
Foundation Physics: Complete Course
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<div class="container">
<h1>Foundation Physics</h1>
<div class="subtitle">Complete Course: From Basic Concepts to Modern Physics</div>
<div class="nav">
<h2>Physics Course Modules</h2>
<div class="nav-grid">
<div class="nav-item" onclick="scrollToSection('fundamentals')">Fundamentals & Units</div>
<div class="nav-item" onclick="scrollToSection('kinematics')">Kinematics</div>
<div class="nav-item" onclick="scrollToSection('dynamics')">Dynamics & Forces</div>
<div class="nav-item" onclick="scrollToSection('energy')">Energy & Work</div>
<div class="nav-item" onclick="scrollToSection('momentum')">Momentum</div>
<div class="nav-item" onclick="scrollToSection('rotation')">Rotational Motion</div>
<div class="nav-item" onclick="scrollToSection('thermal')">Thermodynamics</div>
<div class="nav-item" onclick="scrollToSection('waves')">Waves & Sound</div>
<div class="nav-item" onclick="scrollToSection('electric')">Electricity</div>
<div class="nav-item" onclick="scrollToSection('magnetism')">Magnetism</div>
<div class="nav-item" onclick="scrollToSection('optics')">Light & Optics</div>
<div class="nav-item" onclick="scrollToSection('modern')">Modern Physics</div>
<div class="nav-item" onclick="scrollToSection('glossary')">Glossary</div>
</div>
</div>
<div class="section" id="fundamentals">
<h2>Physics Fundamentals & Units</h2>
<p>Physics is the study of matter, energy, and their interactions. Everything in physics builds from fundamental quantities and mathematical relationships.</p>
<h3>SI Base Units</h3>
<div class="units-table">
<table>
<tr>
<th>Quantity</th>
<th>Unit</th>
<th>Symbol</th>
<th>Dimension</th>
</tr>
<tr>
<td>Length</td>
<td>meter</td>
<td>m</td>
<td>[L]</td>
</tr>
<tr>
<td>Mass</td>
<td>kilogram</td>
<td>kg</td>
<td>[M]</td>
</tr>
<tr>
<td>Time</td>
<td>second</td>
<td>s</td>
<td>[T]</td>
</tr>
<tr>
<td>Electric Current</td>
<td>ampere</td>
<td>A</td>
<td>[I]</td>
</tr>
<tr>
<td>Temperature</td>
<td>kelvin</td>
<td>K</td>
<td>[Θ]</td>
</tr>
<tr>
<td>Amount of Substance</td>
<td>mole</td>
<td>mol</td>
<td>[N]</td>
</tr>
<tr>
<td>Luminous Intensity</td>
<td>candela</td>
<td>cd</td>
<td>[J]</td>
</tr>
</table>
</div>
<h3>Derived Units & Dimensional Analysis</h3>
<div class="formula-box">
<div class="formula-name">Common Derived Units</div>
<div class="formula">
Velocity: m/s = [L][T]^(-1)<br>
Acceleration: m/s² = [L][T]^(-2)<br>
Force: N = kg⋅m/s² = [M][L][T]^(-2)<br>
Energy: J = N⋅m = kg⋅m²/s² = [M][L]²[T]^(-2)<br>
Power: W = J/s = [M][L]²[T]^(-3)
</div>
</div>
<h3>Scientific Notation & Significant Figures</h3>
<div class="concept-box">
<p><strong>Scientific Notation:</strong> Express large/small numbers as a × 10^n where 1 ≤ a < 10</p>
<p><strong>Examples:</strong></p>
<ul>
<li>Speed of light: c = 3.00 × 10⁸ m/s</li>
<li>Planck's constant: h = 6.626 × 10^(-34) J⋅s</li>
<li>Electron mass: m_e = 9.109 × 10^(-31) kg</li>
</ul>
</div>
<div class="tip">
<strong>Dimensional Analysis Tip:</strong> Always check that your equation's dimensions match on both sides. This catches most algebra mistakes and helps verify formula correctness.
</div>
</div>
<div class="section" id="kinematics">
<h2>Kinematics: Motion Without Forces</h2>
<p>Kinematics describes motion using position, velocity, and acceleration without considering the forces that cause motion.</p>
<h3>Basic Kinematic Variables</h3>
<div class="formula-box">
<div class="formula-name">Position, Velocity, and Acceleration</div>
<div class="formula">
Position: x(t)<br>
Velocity: v = dx/dt<br>
Acceleration: a = dv/dt = d²x/dt²
</div>
<div class="formula-vars">
x = position (m)<br>
v = velocity (m/s)<br>
a = acceleration (m/s²)<br>
t = time (s)
</div>
</div>
<h3>Kinematic Equations (Constant Acceleration)</h3>
<div class="formula-box">
<div class="formula-name">The Big Four Kinematic Equations</div>
<div class="formula">
v = v₀ + at<br>
x = x₀ + v₀t + ½at²<br>
v² = v₀² + 2a(x - x₀)<br>
x = x₀ + ½(v₀ + v)t
</div>
<div class="formula-vars">
v₀ = initial velocity<br>
v = final velocity<br>
a = acceleration (constant)<br>
x₀ = initial position<br>
x = final position<br>
t = time
</div>
</div>
<div class="example-box">
<div class="example-title">Example: Free Fall Problem</div>
<p><strong>Problem:</strong> A ball is dropped from a height of 45 meters. How long does it take to hit the ground?</p>
<div class="problem-steps">
<div class="step">
<span class="step-num">Step 1:</span> Identify known values<br>
y₀ = 45 m, y = 0 m, v₀ = 0 m/s, a = -9.8 m/s²
</div>
<div class="step">
<span class="step-num">Step 2:</span> Choose appropriate equation<br>
y = y₀ + v₀t + ½at²
</div>
<div class="step">
<span class="step-num">Step 3:</span> Substitute and solve<br>
0 = 45 + 0 + ½(-9.8)t²<br>
-45 = -4.9t²<br>
t² = 45/4.9 = 9.18<br>
t = 3.03 seconds
</div>
</div>
</div>
<h3>2D Projectile Motion</h3>
<div class="formula-box">
<div class="formula-name">Projectile Motion Components</div>
<div class="formula">
Horizontal: x = v₀ₓt = v₀cos(θ)t<br>
Vertical: y = v₀ᵧt - ½gt² = v₀sin(θ)t - ½gt²<br>
Range: R = (v₀²sin(2θ))/g<br>
Max Height: H = (v₀²sin²(θ))/(2g)
</div>
<div class="formula-vars">
v₀ = initial speed<br>
θ = launch angle<br>
g = 9.8 m/s² (gravitational acceleration)<br>
R = horizontal range<br>
H = maximum height
</div>
</div>
</div>
<div class="section" id="dynamics">
<h2>Dynamics: Forces and Newton's Laws</h2>
<p>Dynamics explains why objects move by studying the forces acting on them. Newton's three laws form the foundation of classical mechanics.</p>
<div class="law-box">
<div class="law-title">Newton's First Law (Law of Inertia)</div>
<p>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.</p>
<div class="formula">ΣF = 0 ⟹ a = 0</div>
</div>
<div class="law-box">
<div class="law-title">Newton's Second Law</div>
<p>The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.</p>
<div class="formula">ΣF = ma</div>
<div class="formula-vars">
ΣF = net force (N)<br>
m = mass (kg)<br>
a = acceleration (m/s²)
</div>
</div>
<div class="law-box">
<div class="law-title">Newton's Third Law</div>
<p>For every action, there is an equal and opposite reaction.</p>
<div class="formula">F₁₂ = -F₂₁</div>
</div>
<h3>Common Forces</h3>
<div class="formula-box">
<div class="formula-name">Force Equations</div>
<div class="formula">
Weight: W = mg<br>
Normal Force: N (perpendicular to surface)<br>
Friction: f = μN<br>
Spring Force: F = -kx<br>
Gravitational: F = G(m₁m₂)/r²
</div>
<div class="formula-vars">
μ = coefficient of friction<br>
k = spring constant (N/m)<br>
x = displacement from equilibrium<br>
G = 6.674 × 10^(-11) N⋅m²/kg²
</div>
</div>
<div class="diagram">
Free Body Diagram Example:
<br><br>
<span class="force-arrow">↑</span> N (Normal Force)
<br>
<span class="force-arrow">←</span> f [BLOCK] F <span class="force-arrow">→</span>
<br>
<span class="force-arrow">↓</span> mg (Weight)
<br><br>
Net Force: ΣF = F - f = ma
</div>
<div class="example-box">
<div class="example-title">Example: Inclined Plane</div>
<p><strong>Problem:</strong> A 10 kg box slides down a 30° incline with μ = 0.2. Find the acceleration.</p>
<div class="problem-steps">
<div class="step">
<span class="step-num">Step 1:</span> Break weight into components<br>
mg∥ = mg sin(30°) = 10 × 9.8 × 0.5 = 49 N (down incline)<br>
mg⊥ = mg cos(30°) = 10 × 9.8 × 0.866 = 84.9 N (into incline)
</div>
<div class="step">
<span class="step-num">Step 2:</span> Find normal force<br>
N = mg⊥ = 84.9 N
</div>
<div class="step">
<span class="step-num">Step 3:</span> Calculate friction<br>
f = μN = 0.2 × 84.9 = 17.0 N (up incline)
</div>
<div class="step">
<span class="step-num">Step 4:</span> Apply Newton's 2nd Law<br>
ΣF = mg∥ - f = 49 - 17 = 32 N<br>
a = ΣF/m = 32/10 = 3.2 m/s²
</div>
</div>
</div>
</div>
<div class="section" id="energy">
<h2>Energy, Work, and Power</h2>
<p>Energy is the capacity to do work. The conservation of energy is one of the most fundamental principles in physics.</p>
<h3>Types of Energy</h3>
<div class="formula-box">
<div class="formula-name">Mechanical Energy</div>
<div class="formula">
Kinetic Energy: KE = ½mv²<br>
Gravitational PE: PE = mgh<br>
Elastic PE: PE = ½kx²<br>
Total Mechanical Energy: E = KE + PE
</div>
<div class="formula-vars">
m = mass (kg)<br>
v = velocity (m/s)<br>
h = height (m)<br>
k = spring constant (N/m)<br>
x = compression/extension (m)
</div>
</div>
<h3>Work and Power</h3>
<div class="formula-box">
<div class="formula-name">Work-Energy Theorem</div>
<div class="formula">
Work: W = F⋅d⋅cos(θ)<br>
W = ΔKE = KE_final - KE_initial<br>
Power: P = W/t = F⋅v<br>
Efficiency: η = (Useful Energy Out)/(Total Energy In)
</div>
<div class="formula-vars">
W = work done (J)<br>
F = force (N)<br>
d = displacement (m)<br>
θ = angle between F and d<br>
P = power (W = J/s)<br>
η = efficiency (dimensionless)
</div>
</div>
<div class="law-box">
<div class="law-title">Conservation of Energy</div>
<p>Energy cannot be created or destroyed, only transformed from one form to another.</p>
<div class="formula">E_initial = E_final</div>
<div class="formula">KE₁ + PE₁ = KE₂ + PE₂ (no friction)</div>
</div>
<div class="example-box">
<div class="example-title">Example: Pendulum Energy</div>
<p><strong>Problem:</strong> A 2 kg pendulum swings from 1.5 m height. What's its speed at the bottom?</p>
<div class="problem-steps">
<div class="step">
<span class="step-num">Step 1:</span> Energy at top<br>
KE₁ = 0 (starts from rest)<br>
PE₁ = mgh = 2 × 9.8 × 1.5 = 29.4 J
</div>
<div class="step">
<span class="step-num">Step 2:</span> Energy at bottom<br>
PE₂ = 0 (reference level)<br>
KE₂ = ½mv² (unknown)
</div>
<div class="step">
<span class="step-num">Step 3:</span> Apply conservation<br>
29.4 = ½ × 2 × v²<br>
v² = 29.4<br>
v = 5.42 m/s
</div>
</div>
</div>
</div>
<div class="section" id="momentum">
<h2>Momentum and Collisions</h2>
<p>Momentum describes the motion of objects and is always conserved in isolated systems, making it crucial for analyzing collisions.</p>
<h3>Linear Momentum</h3>
<div class="formula-box">
<div class="formula-name">Momentum and Impulse</div>
<div class="formula">
Momentum: p = mv<br>
Impulse: J = FΔt = Δp<br>
Conservation: p_total_initial = p_total_final
</div>
<div class="formula-vars">
p = momentum (kg⋅m/s)<br>
m = mass (kg)<br>
v = velocity (m/s)<br>
J = impulse (N⋅s)<br>
F = average force (N)<br>
Δt = time interval (s)
</div>
</div>
<h3>Types of Collisions</h3>
<div class="formula-box">
<div class="formula-name">Collision Analysis</div>
<div class="formula">
Elastic: KE conserved + momentum conserved<br>
v₁f = ((m₁-m₂)/(m₁+m₂))v₁ᵢ + ((2m₂)/(m₁+m₂))v₂ᵢ<br><br>
Inelastic: Only momentum conserved<br>
m₁v₁ᵢ + m₂v₂ᵢ = (m₁+m₂)v_f<br><br>
Coefficient of Restitution: e = -(v₁f - v₂f)/(v₁ᵢ - v₂ᵢ)
</div>
<div class="formula-vars">
e = 1 (perfectly elastic)<br>
e = 0 (perfectly inelastic)<br>
0 < e < 1 (real collisions)
</div>
</div>
</div>
<div class="section" id="rotation">
<h2>Rotational Motion</h2>
<p>Rotational motion involves objects spinning about an axis. The concepts parallel linear motion but use angular quantities.</p>
<h3>Angular Kinematics</h3>
<div class="formula-box">
<div class="formula-name">Rotational Equations</div>
<div class="formula">
Angular Position: θ (radians)<br>
Angular Velocity: ω = dθ/dt<br>
Angular Acceleration: α = dω/dt<br>
ω = ω₀ + αt<br>
θ = θ₀ + ω₀t + ½αt²
</div>
<div class="formula-vars">
θ = angular position (rad)<br>
ω = angular velocity (rad/s)<br>
α = angular acceleration (rad/s²)<br>
1 revolution = 2π radians
</div>
</div>
<h3>Rotational Dynamics</h3>
<div class="formula-box">
<div class="formula-name">Torque and Moment of Inertia</div>
<div class="formula">
Torque: τ = rF sin(θ) = Iα<br>
Moment of Inertia: I = Σmᵢrᵢ²<br>
Rotational KE: KE_rot = ½Iω²<br>
Angular Momentum: L = Iω
</div>
<div class="formula-vars">
τ = torque (N⋅m)<br>
r = distance from axis (m)<br>
I = moment of inertia (kg⋅m²)<br>
L = angular momentum (kg⋅m²/s)
</div>
</div>
</div>
<div class="section" id="thermal">
<h2>Thermodynamics</h2>
<p>Thermodynamics studies heat, temperature, and energy transfer. It bridges mechanics with statistical physics and chemistry.</p>
<h3>Temperature and Heat</h3>
<div class="formula-box">
<div class="formula-name">Temperature Scales</div>
<div class="formula">
Celsius to Kelvin: K = °C + 273.15<br>
Fahrenheit: °F = (9/5)°C + 32<br>
Heat Transfer: Q = mcΔT<br>
Heat Capacity: C = mc
</div>
<div class="formula-vars">
Q = heat energy (J)<br>
m = mass (kg)<br>
c = specific heat capacity (J/kg⋅K)<br>
ΔT = temperature change (K or °C)<br>
C = heat capacity (J/K)
</div>
</div>
<h3>Laws of Thermodynamics</h3>
<div class="law-box">
<div class="law-title">First Law of Thermodynamics</div>
<p>Energy is conserved: the change in internal energy equals heat added minus work done by the system.</p>
<div class="formula">ΔU = Q - W</div>
<div class="formula-vars">
ΔU = change in internal energy (J)<br>
Q = heat added to system (J)<br>
W = work done by system (J)
</div>
</div>
<div class="law-box">
<div class="law-title">Second Law of Thermodynamics</div>
<p>Entropy of an isolated system always increases. Heat flows naturally from hot to cold.</p>
<div class="formula">ΔS ≥ 0 (isolated system)</div>
<div class="formula">Efficiency: η = 1 - T_cold/T_hot (Carnot limit)</div>
</div>
<h3>Ideal Gas Law</h3>
<div class="formula-box">
<div class="formula-name">Gas Properties</div>
<div class="formula">
PV = nRT = NkT<br>
Kinetic Theory: PV = (1/3)Nm⟨v²⟩<br>
Average KE: ⟨KE⟩ = (3/2)kT
</div>
<div class="formula-vars">
P = pressure (Pa)<br>
V = volume (m³)<br>
n = moles, N = number of molecules<br>
R = 8.314 J/mol⋅K, k = 1.381 × 10^(-23) J/K<br>
T = absolute temperature (K)
</div>
</div>
</div>
<div class="section" id="waves">
<h2>Waves and Sound</h2>
<p>Waves transfer energy without transferring matter. Understanding wave properties is essential for sound, light, and quantum mechanics.</p>
<h3>Wave Properties</h3>
<div class="formula-box">
<div class="formula-name">Wave Equation</div>
<div class="formula">
v = fλ<br>
y(x,t) = A sin(kx - ωt + φ)<br>
Wave number: k = 2π/λ<br>
Angular frequency: ω = 2πf
</div>
<div class="formula-vars">
v = wave speed (m/s)<br>
f = frequency (Hz)<br>
λ = wavelength (m)<br>
A = amplitude (m)<br>
k = wave number (rad/m)<br>
ω = angular frequency (rad/s)<br>
φ = phase constant (rad)
</div>
</div>
<h3>Sound Waves</h3>
<div class="formula-box">
<div class="formula-name">Sound Properties</div>
<div class="formula">
Speed in air: v = 343 m/s (at 20°C)<br>
Intensity: I = P/A = (1/2)ρvω²A²<br>
Sound Level: β = 10 log(I/I₀)<br>
Doppler Effect: f' = f((v ± v_observer)/(v ± v_source))
</div>
<div class="formula-vars">
I = intensity (W/m²)<br>
I₀ = 10^(-12) W/m² (threshold of hearing)<br>
β = sound level (dB)<br>
ρ = air density (kg/m³)<br>
+ when approaching, - when receding
</div>
</div>
<div class="concept-box">
<p><strong>Wave Interference:</strong></p>
<ul>
<li><strong>Constructive:</strong> Waves add when in phase (path difference = nλ)</li>
<li><strong>Destructive:</strong> Waves cancel when out of phase (path difference = (n+½)λ)</li>
<li><strong>Standing Waves:</strong> Form when waves reflect and interfere with themselves</li>
</ul>
</div>
</div>
<div class="section" id="electric">
<h2>Electricity and Electric Fields</h2>
<p>Electric phenomena arise from electric charges and their interactions. Understanding electricity is fundamental to modern technology.</p>
<h3>Electric Force and Field</h3>
<div class="formula-box">
<div class="formula-name">Coulomb's Law and Electric Field</div>
<div class="formula">
Electric Force: F = k(q₁q₂)/r²<br>
Electric Field: E = F/q = kQ/r²<br>
Field of Point Charge: E = kq/r²<br>
Force on Charge in Field: F = qE
</div>
<div class="formula-vars">
k = 8.99 × 10⁹ N⋅m²/C² (Coulomb's constant)<br>
q = electric charge (C)<br>
r = distance (m)<br>
E = electric field strength (N/C)
</div>
</div>
<h3>Electric Potential</h3>
<div class="formula-box">
<div class="formula-name">Potential Energy and Voltage</div>
<div class="formula">
Electric PE: U = kq₁q₂/r<br>
Electric Potential: V = U/q = kQ/r<br>
Potential Difference: ΔV = W/q<br>
Relation to Field: E = -dV/dr
</div>
<div class="formula-vars">
U = electric potential energy (J)<br>
V = electric potential (V = J/C)<br>
ΔV = voltage (V)<br>
Work moves charge against field
</div>
</div>
<h3>Electric Circuits</h3>
<div class="formula-box">
<div class="formula-name">Circuit Analysis</div>
<div class="formula">
Ohm's Law: V = IR<br>
Power: P = IV = I²R = V²/R<br>
Series: R_total = R₁ + R₂ + R₃...<br>
Parallel: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃...
</div>
<div class="formula-vars">
V = voltage (V)<br>
I = current (A)<br>
R = resistance (Ω)<br>
P = power (W)
</div>
</div>
<div class="diagram">
Circuit Diagram Symbols:
<br><br>
Battery: ——|+|—————|—|——
<br>
Resistor: ————/\/\/\————
<br>
Current: ————————→————————
<br><br>
Kirchhoff's Laws:
<br>
∑I_in = ∑I_out (current law)
<br>
∑V = 0 (voltage law around loop)
</div>
</div>
<div class="section" id="magnetism">
<h2>Magnetism and Electromagnetic Induction</h2>
<p>Moving electric charges create magnetic fields, and changing magnetic fields create electric fields. This relationship underlies all electromagnetic phenomena.</p>
<h3>Magnetic Force</h3>
<div class="formula-box">
<div class="formula-name">Magnetic Force Laws</div>
<div class="formula">
Force on Moving Charge: F = qvB sin(θ)<br>
Force on Current: F = ILB sin(θ)<br>
Magnetic Field of Wire: B = (μ₀I)/(2πr)<br>
Force Between Wires: F/L = (μ₀I₁I₂)/(2πr)
</div>
<div class="formula-vars">
B = magnetic field (T = Tesla)<br>
μ₀ = 4π × 10^(-7) T⋅m/A<br>
θ = angle between v and B<br>
L = length of conductor (m)
</div>
</div>
<h3>Electromagnetic Induction</h3>
<div class="formula-box">
<div class="formula-name">Faraday's and Lenz's Laws</div>
<div class="formula">
Magnetic Flux: Φ = BA cos(θ)<br>
Faraday's Law: ε = -dΦ/dt<br>
Motional EMF: ε = BLv<br>
Self-Inductance: ε = -L(dI/dt)
</div>
<div class="formula-vars">
Φ = magnetic flux (Wb = Weber)<br>
ε = induced EMF (V)<br>
L = inductance (H = Henry)<br>
Lenz's Law: induced current opposes change
</div>
</div>
</div>
<div class="section" id="optics">
<h2>Light and Optics</h2>
<p>Light exhibits both wave and particle properties. Geometric optics describes light rays, while wave optics explains interference and diffraction.</p>
<h3>Geometric Optics</h3>
<div class="formula-box">
<div class="formula-name">Reflection and Refraction</div>
<div class="formula">
Law of Reflection: θᵢ = θᵣ<br>
Snell's Law: n₁ sin(θ₁) = n₂ sin(θ₂)<br>
Critical Angle: sin(θc) = n₂/n₁<br>
Mirror Equation: 1/f = 1/dₒ + 1/dᵢ
</div>
<div class="formula-vars">
θᵢ = incident angle<br>
θᵣ = reflected angle<br>
n = index of refraction<br>
f = focal length<br>
dₒ = object distance<br>
dᵢ = image distance
</div>
</div>
<h3>Lens Optics</h3>
<div class="formula-box">
<div class="formula-name">Thin Lens Equation</div>
<div class="formula">
Lens Equation: 1/f = 1/dₒ + 1/dᵢ<br>
Magnification: m = -dᵢ/dₒ = hᵢ/hₒ<br>
Lens Maker's Equation: 1/f = (n-1)(1/R₁ - 1/R₂)<br>
Power: P = 1/f (diopters)
</div>
<div class="formula-vars">
m = magnification (dimensionless)<br>
h = height<br>
R = radius of curvature<br>
Positive f = converging lens<br>
Negative f = diverging lens
</div>
</div>
<h3>Wave Optics</h3>
<div class="formula-box">
<div class="formula-name">Interference and Diffraction</div>
<div class="formula">
Double Slit: d sin(θ) = mλ (bright fringes)<br>
Single Slit: a sin(θ) = mλ (dark fringes)<br>
Grating: d sin(θ) = mλ<br>
Resolution: θ = 1.22λ/D (Rayleigh criterion)
</div>
<div class="formula-vars">
d = slit separation<br>
a = slit width<br>
m = order (0, ±1, ±2...)<br>
D = aperture diameter<br>
λ = wavelength
</div>
</div>
</div>
<div class="section" id="modern">
<h2>Modern Physics Introduction</h2>
<p>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.</p>
<h3>Special Relativity</h3>
<div class="formula-box">
<div class="formula-name">Einstein's Relativity</div>
<div class="formula">
Time Dilation: Δt = γΔt₀<br>
Length Contraction: L = L₀/γ<br>
Lorentz Factor: γ = 1/√(1 - v²/c²)<br>
Mass-Energy: E = mc²<br>
Total Energy: E² = (pc)² + (mc²)²
</div>
<div class="formula-vars">
c = 3.00 × 10⁸ m/s (speed of light)<br>
γ = Lorentz factor<br>
Δt₀ = proper time<br>
L₀ = proper length<br>
p = relativistic momentum
</div>
</div>
<h3>Quantum Mechanics Basics</h3>
<div class="formula-box">
<div class="formula-name">Quantum Foundations</div>
<div class="formula">
Planck's Equation: E = hf<br>
de Broglie Wavelength: λ = h/p<br>
Photoelectric Effect: hf = φ + KE_max<br>
Uncertainty Principle: ΔxΔp ≥ ℏ/2
</div>
<div class="formula-vars">
h = 6.626 × 10^(-34) J⋅s (Planck's constant)<br>
ℏ = h/(2π) (reduced Planck's constant)<br>
φ = work function (J)<br>
Δx = position uncertainty<br>
Δp = momentum uncertainty
</div>
</div>
<h3>Atomic Physics</h3>
<div class="formula-box">
<div class="formula-name">Atomic Structure</div>
<div class="formula">
Bohr Model: rₙ = n²(ℏ²/mke²)<br>
Energy Levels: Eₙ = -13.6 eV/n²<br>
Photon Emission: hf = E_initial - E_final<br>
Binding Energy: BE = (Z⋅m_H + N⋅m_n - M_atom)c²
</div>
<div class="formula-vars">
n = principal quantum number<br>
m = electron mass<br>
k = Coulomb's constant<br>
e = elementary charge<br>
Z = atomic number, N = neutron number
</div>
</div>
</div>
<div class="section">
<h2>Problem-Solving Strategy</h2>
<div class="concept-box">
<h3>Universal Physics Problem-Solving Method</h3>
<ol>
<li><strong>Understand:</strong> Read carefully, identify what's given and what's asked</li>
<li><strong>Visualize:</strong> Draw diagrams, free body diagrams, or circuit diagrams</li>
<li><strong>Plan:</strong> Choose relevant principles and equations</li>
<li><strong>Execute:</strong> Apply mathematics carefully, track units</li>
<li><strong>Check:</strong> Verify units, magnitude, and physical reasonableness</li>
</ol>
</div>
<div class="tip">
<strong>Always start with fundamentals!</strong> Most complex problems can be solved using basic principles like F=ma, conservation of energy, or conservation of momentum.
</div>
<div class="warning">
<strong>Common Mistakes:</strong> Forgetting to convert units, using wrong sign conventions, not drawing proper diagrams, confusing scalar and vector quantities, mixing up formulas from different topics.
</div>
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<h4>Quick Reference Calculator</h4>
<p>Use these for quick conversions and checks:</p>
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</div>
<div class="section" id="glossary">
<h2>Physics Glossary</h2>
<div class="glossary">
<div class="glossary-term">Acceleration</div>
<div class="glossary-def">Rate of change of velocity; a = dv/dt. Measured in m/s².</div>
<div class="glossary-term">Angular Momentum</div>
<div class="glossary-def">Rotational analog of linear momentum; L = Iω. Conserved in absence of external torques.</div>
<div class="glossary-term">Electric Field</div>
<div class="glossary-def">Force per unit charge; E = F/q. Describes the electric force environment around charges.</div>
<div class="glossary-term">Energy</div>
<div class="glossary-def">Capacity to do work. Comes in many forms: kinetic, potential, thermal, electromagnetic, etc.</div>
<div class="glossary-term">Entropy</div>
<div class="glossary-def">Measure of disorder in a system. Always increases in isolated systems (2nd Law of Thermodynamics).</div>
<div class="glossary-term">Force</div>
<div class="glossary-def">Push or pull that can change an object's motion; F = ma. Measured in Newtons (N).</div>
<div class="glossary-term">Frequency</div>
<div class="glossary-def">Number of oscillations per second; f = 1/T. Measured in Hertz (Hz).</div>
<div class="glossary-term">Inertia</div>
<div class="glossary-def">Tendency of objects to resist changes in motion. Related to mass in Newton's 1st Law.</div>
<div class="glossary-term">Interference</div>
<div class="glossary-def">Superposition of waves resulting in amplification (constructive) or cancellation (destructive).</div>
<div class="glossary-term">Momentum</div>
<div class="glossary-def">Quantity of motion; p = mv. Conserved in isolated systems.</div>
<div class="glossary-term">Power</div>
<div class="glossary-def">Rate of energy transfer; P = W/t = dE/dt. Measured in Watts (W).</div>
<div class="glossary-term">Potential Energy</div>
<div class="glossary-def">Stored energy due to position or configuration. Can be gravitational, elastic, electric, etc.</div>
<div class="glossary-term">Quantum</div>
<div class="glossary-def">Discrete packet of energy; E = hf. Energy comes in quantized amounts, not continuous.</div>
<div class="glossary-term">Torque</div>
<div class="glossary-def">Rotational force; τ = rF sin(θ). Causes angular acceleration.</div>
<div class="glossary-term">Vector</div>
<div class="glossary-def">Quantity with both magnitude and direction (velocity, force, field). Distinguished from scalars.</div>
<div class="glossary-term">Wavelength</div>
<div class="glossary-def">Distance between adjacent peaks in a wave; λ = v/f. Fundamental wave property.</div>
<div class="glossary-term">Work</div>
<div class="glossary-def">Energy transfer when force acts through distance; W = F⋅d⋅cos(θ). Measured in Joules (J).</div>
</div>
</div>
<div class="section">
<h2>Physics in the Real World</h2>
<div class="concept-box">
<h3>Applications You Use Daily</h3>
<p><strong>Smartphones:</strong> Semiconductors (quantum mechanics), touchscreens (capacitance), GPS (relativity), cameras (optics), speakers (waves)</p>
<p><strong>Transportation:</strong> Internal combustion engines (thermodynamics), electric vehicles (electromagnetic induction), aerodynamics (fluid mechanics)</p>
<p><strong>Medicine:</strong> X-rays (electromagnetic radiation), MRI (nuclear magnetic resonance), ultrasound (wave physics), laser surgery (optics)</p>
<p><strong>Energy:</strong> Solar panels (photoelectric effect), nuclear power (mass-energy equivalence), wind turbines (rotational mechanics)</p>
</div>
<div class="tip">
<strong>Study Strategy:</strong> 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!
</div>
<div class="warning">
<strong>Math Prerequisites:</strong> You'll need algebra, trigonometry, and basic calculus. Don't skip the math - physics IS applied mathematics describing the natural world.
</div>
</div>
<div class="footer">
<p>Foundation Physics Course | From Classical Mechanics to Modern Physics</p>
<p>Master the mathematics of the universe!</p>
</div>
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<h4 style="color: #ff8c00;">Fundamental Physical Constants</h4>
<div style="background: #1a1a1a; padding: 15px; border-radius: 8px; font-family: monospace;">
Speed of light: c = 3.00 × 10⁸ m/s<br>
Planck constant: h = 6.626 × 10⁻³⁴ J⋅s<br>
Gravitational constant: G = 6.674 × 10⁻¹¹ N⋅m²/kg²<br>
Elementary charge: e = 1.602 × 10⁻¹⁹ C<br>
Electron mass: mₑ = 9.109 × 10⁻³¹ kg<br>
Proton mass: mₚ = 1.673 × 10⁻²⁷ kg<br>
Avogadro's number: Nₐ = 6.022 × 10²³ mol⁻¹<br>
Boltzmann constant: k = 1.381 × 10⁻²³ J/K<br>
Gas constant: R = 8.314 J/mol⋅K<br>
Permittivity of free space: ε₀ = 8.854 × 10⁻¹² C²/N⋅m²
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<h4 style="color: #ff8c00;">Essential Unit Conversions</h4>
<div style="background: #1a1a1a; padding: 15px; border-radius: 8px; font-family: monospace;">
<strong>Length:</strong><br>
1 km = 1000 m = 10³ m<br>
1 cm = 0.01 m = 10⁻² m<br>
1 mm = 0.001 m = 10⁻³ m<br>
1 inch = 2.54 cm<br>
1 mile = 1.609 km<br><br>
<strong>Energy:</strong><br>
1 J = 1 N⋅m = 1 kg⋅m²/s²<br>
1 kWh = 3.6 × 10⁶ J<br>
1 eV = 1.602 × 10⁻¹⁹ J<br>
1 calorie = 4.184 J<br><br>
<strong>Time:</strong><br>
1 hour = 3600 s<br>
1 year ≈ 3.156 × 10⁷ s<br><br>
<strong>Angles:</strong><br>
1 revolution = 2π rad = 360°<br>
1 rad = 57.3°
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<h4 style="color: #ff8c00;">Quick Formula Reference</h4>
<div style="background: #1a1a1a; padding: 15px; border-radius: 8px; font-family: monospace;">
<strong>Mechanics:</strong><br>
F = ma, p = mv, KE = ½mv², PE = mgh<br>
W = F⋅d⋅cos(θ), P = W/t<br><br>
<strong>Electricity:</strong><br>
F = kq₁q₂/r², E = kq/r², V = kq/r<br>
V = IR, P = IV<br><br>
<strong>Waves:</strong><br>
v = fλ, f = 1/T<br><br>
<strong>Thermodynamics:</strong><br>
PV = nRT, Q = mcΔT<br>
ΔU = Q - W<br><br>
<strong>Modern:</strong><br>
E = mc², E = hf, λ = h/p
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