Physics Study Guide – Units 1-5

* {
box-sizing: border-box;
margin: 0;
padding: 0;
}

body {
font-family: ‘Segoe UI’, Tahoma, Geneva, Verdana, sans-serif;
background: linear-gradient(135deg, #1a1a2e 0%, #16213e 100%);
min-height: 100vh;
color: #e8e8e8;
line-height: 1.6;
}

.container {
max-width: 1200px;
margin: 0 auto;
padding: 20px;
}

header {
text-align: center;
padding: 30px 0;
background: linear-gradient(135deg, #0f3460 0%, #16213e 100%);
border-radius: 15px;
margin-bottom: 20px;
box-shadow: 0 10px 30px rgba(0,0,0,0.3);
}

header h1 {
font-size: 2.5em;
color: #00d4ff;
text-shadow: 0 0 20px rgba(0,212,255,0.5);
margin-bottom: 10px;
}

header p {
color: #a0a0a0;
font-size: 1.1em;
}

/* Tab Navigation */
.tab-nav {
display: flex;
flex-wrap: wrap;
gap: 5px;
margin-bottom: 20px;
background: #0f3460;
padding: 10px;
border-radius: 10px;
}

.tab-btn {
flex: 1;
min-width: 120px;
padding: 12px 20px;
border: none;
background: #1a1a2e;
color: #a0a0a0;
cursor: pointer;
border-radius: 8px;
font-size: 0.95em;
font-weight: 600;
transition: all 0.3s ease;
}

.tab-btn:hover {
background: #2a2a4e;
color: #00d4ff;
}

.tab-btn.active {
background: linear-gradient(135deg, #00d4ff 0%, #0099cc 100%);
color: #1a1a2e;
box-shadow: 0 5px 15px rgba(0,212,255,0.3);
}

/* Tab Content */
.tab-content {
display: none;
animation: fadeIn 0.4s ease;
}

.tab-content.active {
display: block;
}

@keyframes fadeIn {
from { opacity: 0; transform: translateY(10px); }
to { opacity: 1; transform: translateY(0); }
}

/* Cards */
.card {
background: linear-gradient(135deg, #1e3a5f 0%, #16213e 100%);
border-radius: 15px;
padding: 25px;
margin-bottom: 20px;
box-shadow: 0 10px 30px rgba(0,0,0,0.2);
border: 1px solid rgba(0,212,255,0.1);
}

.card h2 {
color: #00d4ff;
margin-bottom: 15px;
font-size: 1.5em;
display: flex;
align-items: center;
gap: 10px;
}

.card h3 {
color: #4ecdc4;
margin: 20px 0 10px 0;
font-size: 1.2em;
}

/* Expandable Sections */
.expandable {
margin: 10px 0;
border: 1px solid rgba(0,212,255,0.2);
border-radius: 10px;
overflow: hidden;
}

.expandable-header {
background: rgba(0,212,255,0.1);
padding: 15px 20px;
cursor: pointer;
display: flex;
justify-content: space-between;
align-items: center;
transition: background 0.3s ease;
}

.expandable-header:hover {
background: rgba(0,212,255,0.2);
}

.expandable-header h4 {
color: #00d4ff;
font-size: 1.1em;
}

.expandable-icon {
font-size: 1.5em;
color: #00d4ff;
transition: transform 0.3s ease;
}

.expandable.open .expandable-icon {
transform: rotate(45deg);
}

.expandable-content {
max-height: 0;
overflow: hidden;
transition: max-height 0.4s ease;
background: rgba(0,0,0,0.2);
}

.expandable.open .expandable-content {
max-height: 2000px;
}

.expandable-inner {
padding: 20px;
}

/* Lists */
ul, ol {
margin-left: 20px;
margin-bottom: 15px;
}

li {
margin-bottom: 8px;
}

/* Equations */
.equation {
background: rgba(0,212,255,0.1);
padding: 15px 20px;
border-radius: 8px;
font-family: ‘Courier New’, monospace;
font-size: 1.1em;
color: #4ecdc4;
margin: 10px 0;
border-left: 4px solid #00d4ff;
}

/* Warning/Important boxes */
.warning {
background: linear-gradient(135deg, rgba(255,107,107,0.2) 0%, rgba(255,107,107,0.1) 100%);
border: 1px solid #ff6b6b;
border-radius: 10px;
padding: 15px 20px;
margin: 15px 0;
}

.warning h4 {
color: #ff6b6b;
margin-bottom: 10px;
display: flex;
align-items: center;
gap: 8px;
}

.tip {
background: linear-gradient(135deg, rgba(78,205,196,0.2) 0%, rgba(78,205,196,0.1) 100%);
border: 1px solid #4ecdc4;
border-radius: 10px;
padding: 15px 20px;
margin: 15px 0;
}

.tip h4 {
color: #4ecdc4;
margin-bottom: 10px;
}

/* Tables */
table {
width: 100%;
border-collapse: collapse;
margin: 15px 0;
}

th, td {
padding: 12px 15px;
text-align: left;
border: 1px solid rgba(0,212,255,0.2);
}

th {
background: rgba(0,212,255,0.2);
color: #00d4ff;
font-weight: 600;
}

tr:nth-child(even) {
background: rgba(0,0,0,0.2);
}

/* Quiz Section */
.quiz-question {
background: rgba(0,0,0,0.3);
border-radius: 10px;
padding: 20px;
margin: 15px 0;
}

.quiz-question p {
font-weight: 600;
color: #fff;
margin-bottom: 15px;
}

.quiz-options {
display: flex;
flex-direction: column;
gap: 10px;
}

.quiz-option {
padding: 12px 15px;
background: rgba(0,212,255,0.1);
border: 2px solid transparent;
border-radius: 8px;
cursor: pointer;
transition: all 0.3s ease;
}

.quiz-option:hover {
background: rgba(0,212,255,0.2);
border-color: rgba(0,212,255,0.3);
}

.quiz-option.selected {
border-color: #00d4ff;
background: rgba(0,212,255,0.2);
}

.quiz-option.correct {
border-color: #4ecdc4;
background: rgba(78,205,196,0.3);
}

.quiz-option.incorrect {
border-color: #ff6b6b;
background: rgba(255,107,107,0.3);
}

.check-btn {
margin-top: 15px;
padding: 12px 30px;
background: linear-gradient(135deg, #00d4ff 0%, #0099cc 100%);
border: none;
border-radius: 8px;
color: #1a1a2e;
font-weight: 600;
cursor: pointer;
transition: transform 0.2s ease, box-shadow 0.2s ease;
}

.check-btn:hover {
transform: translateY(-2px);
box-shadow: 0 5px 15px rgba(0,212,255,0.4);
}

.feedback {
margin-top: 15px;
padding: 15px;
border-radius: 8px;
display: none;
}

.feedback.show {
display: block;
}

.feedback.correct {
background: rgba(78,205,196,0.2);
border: 1px solid #4ecdc4;
color: #4ecdc4;
}

.feedback.incorrect {
background: rgba(255,107,107,0.2);
border: 1px solid #ff6b6b;
color: #ff6b6b;
}

/* Graph Descriptions */
.graph-box {
display: inline-block;
background: rgba(255,255,255,0.05);
border: 1px solid rgba(0,212,255,0.3);
border-radius: 8px;
padding: 15px;
margin: 10px;
text-align: center;
min-width: 150px;
}

.graph-box .label {
font-size: 0.9em;
color: #a0a0a0;
margin-top: 8px;
}

/* Responsive */
@media (max-width: 768px) {
.tab-btn {
min-width: 80px;
padding: 10px 15px;
font-size: 0.85em;
}

header h1 {
font-size: 1.8em;
}

.card {
padding: 15px;
}
}

/* Print styles */
@media print {
body {
background: white;
color: black;
}

.tab-nav {
display: none;
}

.tab-content {
display: block !important;
}

.expandable-content {
max-height: none !important;
}
}

/* Highlight */
.highlight {
color: #00d4ff;
font-weight: 600;
}

.highlight-warn {
color: #ff6b6b;
font-weight: 600;
}

.highlight-success {
color: #4ecdc4;
font-weight: 600;
}

/* Progress tracker */
.progress-bar {
background: rgba(0,0,0,0.3);
border-radius: 10px;
height: 10px;
margin: 20px 0;
overflow: hidden;
}

.progress-fill {
height: 100%;
background: linear-gradient(90deg, #00d4ff, #4ecdc4);
border-radius: 10px;
transition: width 0.5s ease;
}

🔬 Physics Study Guide

Units 1-5: Energy, Motion, and Forces

⚡ Unit 1: Energy

Energy is the ability to cause a change. It’s not a “thing” itself, but a property of objects in a system.

Energy Storage Modes (E-subscript Notation)

We use “E-subscript” notation to show HOW energy is stored. Remember: it’s all the same energy, just stored differently—like money in different bank accounts!

Energy Stored in MOTION:

Kinetic Energy (E_k) — Energy of a moving object
Thermal Energy (E_th) — Energy of particle motion (temperature)

Energy Stored in POSITION/ARRANGEMENT:

Gravitational Energy (E_g) — Position in Earth’s gravitational field
Elastic Energy (E_el) — Stretched/compressed springs
Chemical Energy (E_ch) — Chemical bonds (batteries, food, fuel)
Physical State Energy (E_ph) — Arrangement of particles

Internal Energy (E_int):

Energy stored in changes to structure/temperature that can’t be easily recovered (like energy “lost” to friction)

Energy Transfer Mechanisms

Energy transfers are PROCESSES (actions), not things. We use the “-ing” form to emphasize they are actions:

Working — Transfer by pushing/pulling (force × distance)
Heating (Q) — Transfer due to temperature difference (hot → cold)
Radiating (R) — Transfer by electromagnetic waves (light)

⚠️ Important Distinction

A system does NOT “have” heat. A high-temperature system stores energy and can transfer it through the process of heating.

System Schemas & Energy Diagrams

System Schema:

Draw circles for each object
Connect with lines to show interactions
Draw boundary around objects IN the system
Objects outside = “surroundings”

Closed System: Energy transfers between modes but stays in system

Open System: Energy can enter or leave

Energy Pie Charts:

Each slice = type of energy storage
Total pie size = total system energy
Closed system → all pies same size
Energy leaving → pies get smaller

Energy Bar Charts (LOL Diagrams):

Left bars = Initial energy storage
Center = Energy flow in/out of system
Right bars = Final energy storage

Conservation of Energy (1st Law of Thermodynamics)

Energy cannot be created or destroyed—only transferred or converted.

ΔE_system = ΔE_g + ΔE_el + ΔE_ph + ΔE_ch + ΔE_k + ΔE_th

ΔE_system = W + Q + R

Initial Energy + Energy In = Final Energy + Energy Out

🚗 Unit 2: Constant Velocity

Key Equations

Velocity: v = Δx / Δt (slope of position-time graph)

Displacement: Δx = v × Δt (area under velocity-time graph)

Position equation: x = x₀ + vt

General form: x_f = x_i + v·Δt

Position vs. Distance (Critical Distinction!)

Position (x)	Distance
Location relative to origin	Total path length traveled
Can be + or −	Always positive
Vector quantity	Scalar quantity

Displacement (Δx) = Change in position = x_f − x_i

Displacement can be + or − and tells you the NET change in position

💡 Think of it like highway exits

Position is like “exit 214” — your location. Distance is how far you drove to get there.

Position-Time Graphs

SLOPE = VELOCITY

Graph Feature	What It Means
Positive slope (going up)	Moving in + direction
Negative slope (going down)	Moving in − direction
Steep slope	Fast motion
Gentle slope	Slow motion
Horizontal line (zero slope)	At rest
Straight line	Constant velocity

💡 Reading x-t Graphs

Describe motion in detail! Example: “The object starts to the right of zero, moves left at constant speed, passes the origin, and continues left.”

Velocity-Time Graphs

AREA UNDER CURVE = DISPLACEMENT

Graph Feature	What It Means
Above x-axis	Moving in + direction
Below x-axis	Moving in − direction
Horizontal line	Constant velocity
On the x-axis (v=0)	At rest

⚠️ Important

The v-t graph does NOT tell you the starting position! Two different x-t graphs can have the same v-t graph.

Motion Maps

Dots show position at equal time intervals
Equally spaced dots = constant velocity
Velocity vectors all same length (for constant v)
No acceleration vectors for constant velocity

⚠️ Common Mistake

If object B moves faster than A, the dots should be farther apart AND the velocity vectors should be longer. Both must be true!

Momentum

Momentum: p = mv

Conservation: p₁ᵢ + p₂ᵢ = p₁f + p₂f

Sticking collision: m₁v₁ + m₂v₂ = (m₁ + m₂)v_f

💡 Remember

Direction matters! Define + and − directions first. Objects moving in opposite directions have opposite-signed momenta.

🚀 Unit 3: Uniformly Accelerated Motion

Key Equations

Acceleration: a = Δv / Δt (slope of v-t graph)

Final velocity: v_f = v_i + aΔt

Displacement: Δx = v_iΔt + ½a(Δt)²

Average velocity: v̄ = (v_i + v_f) / 2 (only for constant a!)

Units: m/s² means “meters per second, per second” — velocity changes by this amount each second.

Instantaneous vs. Average Velocity

Average velocity = total displacement / total time (slope of secant line)

Instantaneous velocity = velocity at a specific moment (slope of tangent line)

Finding Instantaneous Velocity from a Curved x-t Graph:

Method 1: Tangent Line

Draw a line that just touches the curve at that point. Find its slope.

Method 2: Surrounding Points

Use points just before and after. Calculate Δx/Δt for this small interval.

💡 Key Insight

As you shrink the time interval smaller and smaller, the secant line approaches the tangent line. The average velocity over a tiny interval ≈ instantaneous velocity.

Position-Time Graphs (Accelerated Motion)

Graph Feature	What It Means
Curved (parabolic)	Object is accelerating
Curve opens upward (concave up)	Positive acceleration
Curve opens downward (concave down)	Negative acceleration
Slope at any point	Instantaneous velocity
Slope getting steeper	Speed increasing

Velocity-Time Graphs (Accelerated Motion)

SLOPE = ACCELERATION

AREA = DISPLACEMENT

Graph Feature	What It Means
Straight diagonal line	Constant acceleration
Line with + slope	Positive acceleration
Line with − slope	Negative acceleration
Line crosses x-axis	Object changes direction

🚨 CRITICAL MISCONCEPTION 🚨

“Positive acceleration means speeding up” — THIS IS FALSE!

What ACTUALLY determines speeding up vs. slowing down:

SPEEDING UP: Velocity and acceleration have the SAME sign
SLOWING DOWN: Velocity and acceleration have OPPOSITE signs

Velocity	Acceleration	Result
+5 m/s	+2 m/s²	SPEEDING UP
−5 m/s	−2 m/s²	SPEEDING UP
+5 m/s	−2 m/s²	SLOWING DOWN
−5 m/s	+2 m/s²	SLOWING DOWN

Avoid the term “deceleration” — it causes confusion!

Cart on Ramp Scenario

Scenario: Cart pushed up ramp toward motion detector at top

Quantity	Going Up	At Top	Coming Down
Position	Decreasing	Minimum	Increasing
Velocity	Negative (→ detector)	Zero	Positive (← away)
Acceleration	CONSTANT AND POSITIVE the entire time!

💡 Energy Connection

Going up: E_k → E_g | Coming down: E_g → E_k

⚖️ Unit 4: Balanced Forces

Types of Forces

Force	Symbol	Description
Gravitational	F_g	Earth pulling object down (F_g = mg)
Normal	F_N	Perpendicular push from surface
Tension	F_T	Pull through rope/string/cable
Friction	F_f	Resists sliding between surfaces
Applied	F_A	External push/pull by person/object

Drawing Force Diagrams (Free Body Diagrams)

Represent object as a dot or simple shape
Draw ONLY forces acting ON the object
Draw arrows from center pointing outward
Label each force (F_g, F_N, F_T, etc.)
Arrow length shows relative magnitude
Use tick marks to show equal forces

⚠️ Common Mistakes

Including forces the object exerts ON others (wrong!)
Including “inertia” as a force (it’s NOT a force!)
Forgetting the normal force

Balanced Forces = Equilibrium

When all forces cancel out:

ΣF = 0 (net force is zero)

ΣF_x = 0 and ΣF_y = 0

Object is either:

At rest, OR
Moving with constant velocity

Acceleration = 0

Common Balanced Force Scenarios

Scenario	Key Relationship
Object hanging from string	F_T = F_g
Object at rest on surface	F_N = F_g
Pushed but not moving	F_f = F_A (horizontal) F_N = F_g (vertical)
Block between two strings	F_T(top) = F_g + F_T(bottom)
Chain of hanging objects	Tension supports all weight below

🚨 INERTIA IS NOT A FORCE! 🚨

Inertia is the tendency of an object to resist changes in motion. It is a property, not a force.

NEVER include “inertia” in a force diagram!

💥 Unit 5: Unbalanced Forces (Newton’s 2nd Law)

🔗 The Big Connection: Forces ↔ Motion ↔ Energy

Balanced forces → Constant velocity (or rest)
Unbalanced forces → Acceleration
Forces through distance → Energy transfer (Working)

Newton’s Second Law

ΣF = ma

a = ΣF / m

What happens when you change things:

Change	Effect on Acceleration
↑ Mass (same force)	↓ Acceleration
↑ Force (same mass)	↑ Acceleration
Double both	Same acceleration

Problem-Solving Strategy

Draw a force diagram showing all forces
Choose a positive direction
Write ΣF = ma for each direction
Substitute known values
Solve for the unknown

The Elevator Problem

Why do grocery bag handles sometimes rip? It depends on how the bag accelerates!

Standing on a scale in an elevator:

Elevator Motion	Forces	You Feel…
Accelerating UP	F_N > F_g	HEAVIER
Accelerating DOWN	F_N < F_g	LIGHTER
Constant velocity (any direction)	F_N = F_g	NORMAL

💡 Key Insight

You can’t feel which direction you’re MOVING—only which direction you’re ACCELERATING!

Cable tension equations:

Accelerating up: F_T = m(g + a)

Accelerating down: F_T = m(g − a)

Falling Objects

All objects fall with the same acceleration (g ≈ 10 m/s²) when air resistance is ignored.

Why? Heavier objects have MORE gravitational force but also MORE mass:

a = F_g/m = mg/m = g

The mass cancels out!

Energy Connections

Gravitational Energy: E_g = mgh

Elastic Energy: E_e = ½kx²

Spring Force: F = kx

When forces act on objects through distances, energy is transferred (Working).

🎯 Self-Quiz

Test your understanding! Click on your answer, then check.

1. A ball is dropped from rest. As it falls (ignoring air resistance), which describes the energy changes?

E_g increases, E_k decreases

E_g decreases, E_k increases, total stays same

E_g decreases, E_k increases, total decreases

Both E_g and E_k increase

2. On a position vs. time graph, a straight line with negative slope means:

Object is at rest

Object is speeding up in negative direction

Object is moving at constant velocity in negative direction

Object is slowing down

3. An object has velocity = −8 m/s and acceleration = +2 m/s². The object is:

Speeding up in the negative direction

Slowing down (moving negative, accelerating positive = opposite signs)

Speeding up in the positive direction

At rest

4. A book sits motionless on a table. The forces on the book are:

Only gravitational force

Only normal force

Gravitational force and normal force (balanced)

Gravitational, normal, and inertia forces

5. A person stands on a scale in an elevator. The scale reads MORE than their normal weight. The elevator is:

Moving up at constant speed

Moving down at constant speed

Accelerating upward

Accelerating downward

6. Which of the following is NOT a force?

Tension

Inertia

Friction

Normal force

7. The area under a velocity-time graph represents:

Displacement

Acceleration

Average velocity

Final position

8. A cart is pushed up a ramp toward a motion detector at the top. After the push, while the cart is on the ramp, the acceleration is:

Positive going up, negative going down

Negative going up, positive going down

Zero at the highest point

Constant and positive the entire time

📋 Formula Sheet

Kinematics (Motion)

Quantity	Formula	Graph Connection
Velocity	v = Δx / Δt	Slope of x-t graph
Acceleration	a = Δv / Δt	Slope of v-t graph
Displacement	Δx = vΔt (constant v) Δx = v_iΔt + ½a(Δt)²	Area under v-t graph
Final velocity	v_f = v_i + aΔt	—
Average velocity	v̄ = (v_i + v_f) / 2	Only for constant a

Forces (Dynamics)

Quantity	Formula
Weight (gravitational force)	F_g = mg
Newton’s 2nd Law	ΣF = ma
Equilibrium	ΣF = 0
Spring force	F = kx

Energy

Type	Formula
Gravitational potential energy	E_g = mgh
Elastic potential energy	E_e = ½kx²
Conservation of energy	E_initial + E_in = E_final + E_out
1st Law of Thermodynamics	ΔE_system = W + Q + R

Momentum

Quantity	Formula
Momentum	p = mv
Conservation	p_1i + p_2i = p_1f + p_2f

Constants

g = 10 m/s² (use this unless told otherwise)

// Tab switching
document.querySelectorAll(‘.tab-btn’).forEach(btn => {
btn.addEventListener(‘click’, () => {
// Remove active from all tabs and content
document.querySelectorAll(‘.tab-btn’).forEach(b => b.classList.remove(‘active’));
document.querySelectorAll(‘.tab-content’).forEach(c => c.classList.remove(‘active’));

// Add active to clicked tab and corresponding content
btn.classList.add(‘active’);
document.getElementById(btn.dataset.tab).classList.add(‘active’);
});
});

// Expandable sections
document.querySelectorAll(‘.expandable-header’).forEach(header => {
header.addEventListener(‘click’, () => {
header.parentElement.classList.toggle(‘open’);
});
});

// Quiz functionality
document.querySelectorAll(‘.quiz-option’).forEach(option => {
option.addEventListener(‘click’, () => {
// Remove selected from siblings
option.parentElement.querySelectorAll(‘.quiz-option’).forEach(o => {
o.classList.remove(‘selected’, ‘correct’, ‘incorrect’);
});
option.classList.add(‘selected’);

// Hide feedback
option.closest(‘.quiz-question’).querySelector(‘.feedback’).classList.remove(‘show’);
});
});

function checkAnswer(btn) {
const question = btn.closest(‘.quiz-question’);
const correct = question.dataset.correct;
const selected = question.querySelector(‘.quiz-option.selected’);
const feedback = question.querySelector(‘.feedback’);

if (!selected) {
feedback.textContent = ‘Please select an answer first!’;
feedback.className = ‘feedback show incorrect’;
return;
}

const selectedValue = selected.dataset.value;

if (selectedValue === correct) {
selected.classList.add(‘correct’);
feedback.textContent = ‘✓ Correct! Great job!’;
feedback.className = ‘feedback show correct’;
} else {
selected.classList.add(‘incorrect’);
// Highlight correct answer
question.querySelectorAll(‘.quiz-option’).forEach(o => {
if (o.dataset.value === correct) {
o.classList.add(‘correct’);
}
});
feedback.textContent = ‘✗ Not quite. The correct answer is highlighted in green.’;
feedback.className = ‘feedback show incorrect’;
}
}