Mr. Scandrett's ClassroomOS

Physics · Lesson 04

Newton's Laws of Motion

Force & Motion F = ma Inertia Action & Reaction K–12

In 1687, Isaac Newton published three simple rules that explain how everything moves — from a rolling marble to a rocket heading to the Moon. Over 300 years later, engineers still use these same three laws every day.

Who Was Isaac Newton?

Portrait of Isaac Newton

Isaac Newton (1643–1727) was an English mathematician and physicist who changed science forever. According to legend, watching an apple fall from a tree made him wonder: why do things fall down? That question led him to develop the laws of gravity and motion. He published his three laws of motion in his masterwork Principia Mathematica in 1687. Newton also invented calculus, designed the first reflecting telescope, and explained why white light contains every color of the rainbow. Scientists consider him one of the most influential people who ever lived.

The Three Laws at a Glance

Newton described three rules that govern how objects move and how forces change that motion. Together, they explain almost every motion you can observe with the naked eye.

First Law
Inertia
Objects resist changes in motion — still things stay still, moving things keep moving.
Second Law
F = ma
Force equals mass times acceleration — push harder or use less mass to go faster.
Third Law
Action–Reaction
Every force has an equal and opposite force pushing back the other way.

First Law — The Law of Inertia

1

Newton's First Law

"An object at rest stays at rest, and an object in motion stays in motion at the same speed and in the same direction, unless acted upon by an unbalanced external force."

In plain English: things don't change what they're doing on their own. You need to push or pull something to make it start, stop, speed up, slow down, or turn.

What is Inertia?

Inertia is the tendency of an object to resist any change in its state of motion. The more mass an object has, the more inertia it has — meaning the harder it is to start moving, stop, or change direction.

Think about pushing an empty shopping cart versus a full one. The full cart has more mass, so it has more inertia — it is much harder to get moving, and much harder to stop once it is rolling.

Everyday test: Slide a book across a table. It slows down and stops — not because of inertia, but because friction is the external force acting against it. In deep space, far from any friction or air resistance, that same book would keep sliding forever at exactly the same speed. That is inertia at work.

Real-World Examples of the First Law

🚗
Seatbelts When a car brakes hard, your body wants to keep moving forward (inertia). The seatbelt applies the external force that stops you — not the car door.
🏒
Hockey Puck A puck on ice has very little friction. Once hit, it glides for a long time — nearly unchanged motion, just like Newton's First Law predicts.
🧺
Tablecloth Trick Pull a tablecloth out fast and the dishes stay put. The dishes have inertia — they resist the sudden horizontal force and barely move.

Second Law — Force, Mass, and Acceleration

2

Newton's Second Law

"The acceleration of an object depends directly on the net force acting on it, and inversely on its mass."

The bigger the force you apply, the faster the object accelerates. The heavier the object, the less it accelerates for the same force. This relationship is captured in the most famous equation in mechanics:

Understanding the Equation

The equation F = ma can be rearranged to find any of the three values:

To find… Use this formula Example
Force (F) F = m × a 2 kg × 3 m/s² = 6 N
Acceleration (a) a = F ÷ m 10 N ÷ 5 kg = 2 m/s²
Mass (m) m = F ÷ a 12 N ÷ 4 m/s² = 3 kg

Real-World Examples of the Second Law

⚽
Kicking a Ball Kick harder (more force) and the ball accelerates faster. The same kick on a bowling ball barely moves it — more mass means less acceleration.
🚀
Rocket Launch Rockets burn fuel (reducing mass) while producing thrust (constant force). As mass drops, acceleration increases — that's why rockets speed up as they climb.
🚲
Cycling Pedalling harder increases force and accelerates the bike. A loaded cargo bike is harder to accelerate than an empty one — same force, more mass.
What is a Newton? One Newton (1 N) is the force needed to accelerate a 1 kg object at 1 m/s². To feel roughly 1 N, hold a small apple — the Earth pulls it down with about 1 N of gravitational force. The unit is named after Isaac Newton himself.

Legend of the Apple Lab

Use one famous apple to walk through all three laws: first it rests, then a shake starts the motion, and finally the impact reveals an action-reaction pair.

Newton's Apple Garden

A story-driven "What If?" lab for inertia, F = ma, and action-reaction.

1kg
Apple pushes on Newton
Newton pushes back on apple
BONK!
Law 1: The apple stays at rest until an outside force shakes the branch.
Step 1: Apply Force
Step 3: Observe
Mass 1 kg
Gravity 9.8 m/s²
Impact Story Gentle bonk

Third Law — Action and Reaction

3

Newton's Third Law

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

Whenever one object pushes or pulls on another, the second object pushes or pulls back with the same amount of force — but in the opposite direction. Forces always come in pairs.

The Key Insight: Forces Always Come in Pairs

You can never have just one force. Every force is part of an action-reaction pair acting on two different objects. The forces are equal in size but opposite in direction.

Important: The two paired forces act on different objects, so they do not cancel each other out. When you push against a wall, you push the wall forward and the wall pushes you backward — those forces act on two different things (you and the wall), so the wall does not move (it is attached to the Earth).

The Apple "Bonk" — Law 3 in Action

When the apple reaches Newton's head, the contact force works both ways. The apple pushes down on Newton's head, and Newton's head pushes up on the apple with an equal force in the opposite direction. They do not cancel because each force acts on a different object.

Real-World Examples of the Third Law

🏊
Swimming Your hands push backward against the water (action). The water pushes your body forward (reaction). That's how you move through the pool.
🚤
Jumping Off a Boat You push backward on the boat (action) as you jump forward. The boat pushes you forward — but also slides backward away from the dock (reaction).
🛹
Pushing Off on Skateboards When two students on skateboards push against each other, each person exerts a force on the other (action). Both riders roll away in opposite directions with equal and opposite forces (reaction).

Newton's Laws in the Real World

These three laws are not just classroom theory — engineers use them constantly to design everything from cars to spacecraft.

🛸
Spacecraft Navigation NASA engineers use all three laws to plan every rocket burn. Law 1 keeps a spacecraft coasting between planets. Law 2 calculates how much thrust is needed for a course correction. Law 3 is why rocket engines work at all. Law 1 Law 2 Law 3
🚗
Car Safety Design Crumple zones slow the deceleration of a crash (Law 2: spreading force over more time reduces acceleration). Airbags and seatbelts stop your body's inertia (Law 1) from throwing you through the windshield. Law 1 Law 2
🏗️
Building Structures Every beam in a building must handle pairs of forces (Law 3). A floor beam pushes down on its supports; the supports push up with equal force. Engineers calculate these to make sure nothing snaps. Law 3
⚽
Sports Science A sprinter explodes off starting blocks by pushing backward against them (Law 3). A heavier shot-put requires more force to throw the same distance (Law 2). A ball keeps rolling on smooth ground (Law 1). Law 1 Law 2 Law 3

Practice Problems

Use F = ma and its rearrangements. Round to one decimal place where needed.

Easy1. A force of 30 N acts on a 6 kg box. What is the acceleration? (a = F ÷ m)

Hint: a = 30 ÷ 6 = 5 m/s²

Easy2. A 4 kg object accelerates at 3 m/s². What force caused this? (F = m × a)

Hint: F = 4 × 3 = 12 N

Medium3. A 10 N force produces an acceleration of 2.5 m/s². What is the mass of the object? (m = F ÷ a)

Hint: m = 10 ÷ 2.5 = 4 kg

Medium4. A car of mass 1,200 kg accelerates at 3 m/s². What net force does the engine produce?

Hint: F = 1,200 × 3 = 3,600 N

Challenge5. A rocket weighs 500,000 kg at launch. Its engines produce 7,500,000 N of thrust. What is its initial acceleration? (Ignore gravity for this calculation.)

Hint: a = 7,500,000 ÷ 500,000 = 15 m/s²

Challenge6. A swimmer pushes against the pool wall with a force of 180 N. By Newton's Third Law, with what force does the wall push the swimmer back?

Hint: Newton's Third Law — equal and opposite. Same force: 180 N.