Newton’s Laws of Motion

Introduction

Newton’s Laws of Motion explain how forces change motion. They are the foundation of classical mechanics and are used to understand everyday situations such as walking, cycling, sports, vehicle safety, machines, and spacecraft. In this Grades 9–10 aiMOOC, you will connect observations, diagrams, equations, experiments, and explanations.

Newton’s three laws connect three central ideas: an object’s motion, the forces acting on it, and the interactions between objects. The laws were published by Isaac Newton in 1687 in Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). Modern physics has shown that Newtonian mechanics is an excellent approximation for many ordinary, macroscopic objects moving much more slowly than the speed of light.

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Learning Goals

By the end of this course, you should be able to explain force, mass, acceleration, inertia, and net force; distinguish balanced from unbalanced forces; apply the three laws to real situations; calculate force, mass, or acceleration using Newton’s second law; draw and interpret a free-body diagram; identify valid third-law force pairs; and design simple investigations that test predictions about motion.

Before You Start: Motion and Force

Velocity describes both speed and direction. Acceleration is any change in velocity, so an object accelerates when it speeds up, slows down, or changes direction. A force is an interaction that can change motion. Force is a vector, which means it has both magnitude and direction.

The net force is the vector sum of all external forces acting on a chosen object or system. If the forces balance, the net force is zero. Zero net force does not necessarily mean zero motion; it means zero acceleration.

Common forces include gravity, normal force, friction, tension, drag, thrust, and applied pushes or pulls. The SI unit of force is the newton, written N.

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Newton’s First Law: Inertia

Newton’s first law states that an object at rest remains at rest, and an object moving with constant velocity continues moving with constant velocity, unless a net external force acts on it. This law is often called the law of inertia.

Inertia is the tendency of an object to resist changes in its velocity. Mass is a measure of inertia: an object with greater mass is harder to accelerate than an object with smaller mass when the same net force is applied.

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Balanced Forces and Constant Velocity

Imagine a book resting on a level table. Gravity pulls downward while the table’s normal force pushes upward. If these forces have equal magnitude, the net vertical force is zero, so the book has no vertical acceleration.

Now imagine a puck gliding across nearly frictionless ice. If the net force becomes approximately zero, the puck keeps moving at nearly constant velocity. In everyday life, friction often hides this behavior because it produces a force opposite the direction of sliding.

Key idea: Motion does not require a continuing net force. A change in velocity requires a nonzero net force.

First-Law Examples

A passenger’s body tends to keep moving forward when a car suddenly slows, which is why seat belts are essential. A tablecloth can sometimes be pulled quickly from under dishes because the dishes resist changes in their state of motion. A spacecraft far from strong external influences can continue moving without engines constantly pushing it forward.

In each example, identify the object you are studying, describe its initial velocity, and then ask whether the net external force is zero or nonzero.

Newton’s Second Law: Force, Mass, and Acceleration

Newton’s second law gives a quantitative relationship between net force, mass, and acceleration. For an object of constant mass:

${\vec{F}}_{net} = m \vec{a}$

The acceleration points in the same direction as the net force. You can also rearrange the equation:

$\vec{a} = \frac{{\vec{F}}_{net}}{m}$

This shows two important patterns. With the same mass, a larger net force produces a larger acceleration. With the same net force, a larger mass produces a smaller acceleration.

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The Unit Newton

One newton is the force needed to accelerate a mass of one kilogram at one metre per second squared:

$1 N = 1 k g \cdot m / s^{2}$

Always distinguish mass from weight. Mass is measured in kilograms and describes inertia. Weight is a force caused by gravity. Near Earth’s surface, the magnitude of weight can be estimated with:

$W = m g$

where $g \approx 9.8 m / s^{2}$ .

Worked Example: Finding Acceleration

A 3 kg cart experiences a net horizontal force of 12 N. Using $a = F_{net} / m$ :

$a = \frac{12 N}{3 k g} = 4 m / s^{2}$

The cart accelerates at 4 m/s² in the direction of the net force. Notice that you use the net force, not just one force that happens to act on the cart.

Worked Example: Several Forces

Suppose one student pushes a box to the right with 40 N while friction acts to the left with 10 N. The horizontal net force is 30 N to the right. If the box has a mass of 15 kg, then:

$a = \frac{30 N}{15 k g} = 2 m / s^{2}$

The box accelerates to the right. The normal force and weight may balance vertically while the horizontal forces remain unbalanced.

Newton’s Third Law: Interaction Pairs

Newton’s third law states that when object A exerts a force on object B, object B simultaneously exerts a force of equal magnitude and opposite direction on object A.

A third-law pair has four important features: the two forces arise from the same interaction, have equal magnitudes, point in opposite directions, and act on different objects. Because they act on different objects, the two forces do not cancel each other in the free-body diagram of either single object.

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Third-Law Examples

When you walk, your foot pushes the ground backward and the ground pushes your foot forward. When a swimmer pushes water backward, the water pushes the swimmer forward. In a balloon rocket, the balloon pushes escaping air backward and the escaping air pushes the balloon forward. A rocket does not need air outside it to push against; its thrust comes from the interaction between the rocket and its expelled exhaust.

When a book rests on a table, the normal force on the book and the book’s weight are not a third-law pair because both forces act on the same object. Their partners act on different objects: Earth is pulled by the book, and the table is pushed by the book.

Free-Body Diagrams and Net Force

A free-body diagram shows one chosen object separated from its surroundings, with arrows representing the external forces acting on that object. The arrow direction shows force direction, and arrow length can be used to represent relative magnitude.

To construct a useful diagram, choose the system first. Then identify interactions with the surroundings, draw only the external forces acting on the chosen system, label each force clearly, and use the diagram to determine the net force.

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Example: Box on a Floor

For a box pushed across a horizontal floor, the forces may include weight downward, normal force upward, applied force forward, and friction backward. If the upward and downward forces balance but the forward applied force is larger than friction, the net force is horizontal and the box accelerates horizontally.

This is why free-body diagrams are powerful: they turn a complex scene into a clear force model.

Connecting the Three Laws

The laws work together rather than as isolated rules. The first law describes what happens when net force is zero. The second law predicts the acceleration when net force is nonzero. The third law explains how forces arise through interactions between objects.

For example, when a skateboarder pushes backward on the ground, the ground pushes forward on the skateboarder according to the third law. That forward external force contributes to the skateboarder’s net force. The second law then relates that net force to acceleration. Once the net force returns to zero, the first law predicts constant velocity.

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A Newton’s cradle provides a striking collision example. The balls exert forces on one another during contact. Its motion is best understood by combining interaction forces with the conservation of momentum and, for a good approximation, mechanical energy.

Common Misconceptions

Misconception: An object must have a net force in the direction it is moving. Correction: An object can move at constant velocity with zero net force.

Misconception: Heavier objects always accelerate more when pushed. Correction: Acceleration depends on both net force and mass. With the same net force, greater mass produces less acceleration.

Misconception: Third-law forces cancel each other. Correction: They act on different objects. Forces cancel only when opposite forces acting on the same chosen object sum to zero.

Misconception: If an object is not moving, no forces act on it. Correction: An object at rest can have several forces acting on it as long as their vector sum is zero.

A Problem-Solving Strategy

When you solve a force problem, begin by identifying the object or system. Draw a free-body diagram, choose positive directions, and add forces with signs that match those directions. Calculate the net force in each direction. Then apply Newton’s second law and check whether the direction, units, and size of the result make physical sense.

For many Grades 9–10 problems, horizontal and vertical directions can be treated separately. A box can have zero vertical acceleration while accelerating horizontally.

Safe Classroom Investigations

You can investigate Newton’s laws with simple, low-risk equipment such as toy carts, string, masses, spring scales, balloons, smooth boards, and stopwatches or motion sensors. Keep moving objects at low speed, keep ramps low, use a clear path, and protect eyes during balloon activities.

One useful investigation is to apply different measured forces to the same cart and compare the resulting accelerations. Another is to keep the applied force approximately constant while changing the cart’s mass. Your graphs should reveal the relationships predicted by the second law.

Where Newton’s Laws Work Well—and Their Limits

Newton’s laws successfully describe a huge range of everyday and engineering motion. They are especially effective for macroscopic objects moving far below the speed of light.

At extremely high speeds, special relativity provides a more accurate framework. At atomic and subatomic scales, quantum mechanics becomes necessary. Learning these limits does not make Newton’s laws less useful; it shows that scientific models have domains in which they work best.

Interactive Tasks

Quiz: Test Your Knowledge

What happens to an object’s velocity when the net external force is zero? (It remains constant) (!It must become zero) (!It always increases) (!It always changes direction)

What is inertia? (The tendency to resist changes in velocity) (!The force that always points upward) (!The rate at which distance changes) (!The energy stored in a moving object)

What is the SI unit of force? (Newton) (!Kilogram) (!Metre) (!Second)

A 3 kg cart has a net force of 12 N. What is its acceleration? (4 metres per second squared) (!9 metres per second squared) (!15 metres per second squared) (!36 metres per second squared)

If the same net force acts on twice the mass, what happens to the acceleration? (It is halved) (!It is doubled) (!It stays the same) (!It becomes zero)

A book rests on a level table with no vertical acceleration. How are the upward normal force and downward weight related? (They have equal magnitude) (!The normal force is always larger) (!The weight is always zero) (!They point in the same direction)

Which statement is a correct Newton’s third-law pair during walking? (The foot pushes the ground backward and the ground pushes the foot forward) (!The foot pushes the ground backward and gravity pulls the foot downward) (!Gravity pulls the person down and friction pushes the person forward) (!The normal force and weight on the person are a third-law pair)

Why do Newton’s third-law forces not cancel each other on one free-body diagram? (They act on different objects) (!They act at different times) (!They have different magnitudes) (!They always point in the same direction)

Which statement correctly compares mass and weight? (Mass measures inertia while weight is a force) (!Mass and weight are the same quantity) (!Mass is measured in newtons) (!Weight never depends on gravity)

What should a free-body diagram show? (All external forces acting on the chosen object) (!Only forces that make the object move) (!Every object in the entire scene) (!Only the largest force)

Memory Game

Inertia	Resistance to a change in velocity
Net force	Vector sum of external forces
Acceleration	Rate of change of velocity
Friction	Force that opposes relative sliding
Normal force	Contact force perpendicular to a surface
Newton	SI unit of force

Drag and Drop

Match the correct terms.	Topic
Law of inertia	Constant velocity when net force is zero
Force mass relation	Acceleration depends on net force and mass
Interaction pair	Equal and opposite forces on different objects
Free-body diagram	External forces on one chosen system
Balanced forces	Zero vector sum of forces

...

Crossword Puzzle

Inertia	What tendency makes an object resist a change in velocity?
Newton	What is the SI unit of force?
Acceleration	What quantity describes a change in velocity per unit time?
Friction	What force opposes relative sliding between surfaces?
Reaction	What word is often used for the partner force in a third-law pair?
Equilibrium	What state has zero net force and therefore zero acceleration?

LearningApps

Cloze Text

Newton’s first law says that velocity remains

when the net external force is zero. The tendency to resist changes in velocity is called

. A force has both magnitude and

. The vector sum of external forces is the

. Newton’s second law connects net force, mass, and

. For constant mass, the relationship is commonly written as Fnet equals m times

. The SI unit of force is the

. Weight is the force produced by

. In a third-law interaction, the forces have equal magnitude and opposite

. The two third-law forces act on different

. A diagram showing external forces on one chosen system is a

. When opposite forces on one object sum to zero, the forces are

.

Open-Ended Tasks

Easy

Motion Observation Journal: Observe three everyday motions such as a bicycle starting, a ball rolling, or a door opening; write which object changes velocity and identify the likely net force causing each change.
Force Diagram Poster: Create a clear poster showing a free-body diagram of a book on a table and explain the direction and role of weight and normal force.
Inertia Demonstration: Design and safely perform a simple coin-and-card or toy-cart demonstration of inertia, then write a short explanation linking your observation to Newton’s first law.
Physics Photo Hunt: Take or draw four images of real-life force situations and add English captions naming the object, relevant forces, and whether the net force is zero.

Standard

Cart Force Experiment: Use a toy cart or dynamics cart to compare motion under two or more applied forces while keeping mass constant; record observations and explain the trend using Newton’s second law.
Mass and Acceleration Investigation: Keep the applied force as similar as possible while changing cart mass; collect data, make a graph, and explain whether the results agree with the inverse relationship between mass and acceleration.
Third-Law Interview: Interview a coach, cyclist, swimmer, mechanic, or science teacher about a real situation involving pushes and pulls; identify one genuine third-law force pair from the interview and justify your choice.
Newton Video Explainer: Produce a short video in English that explains one law using a safe real-life demonstration, a labeled diagram, and one common misconception that you correct.

Advanced

Free-Body Diagram Investigation: Analyze a multi-force situation such as a sled, bicycle, or box on a ramp; create accurate free-body diagrams, choose axes, and calculate or estimate the net force.
Balloon Rocket Engineering: Build a safe balloon rocket on a string, test one design variable, collect repeated measurements, and explain the motion using both Newton’s second and third laws.
Museum or Laboratory Field Study: Visit a science museum, school laboratory, workshop, or engineering site and document at least three examples where Newton’s laws help explain the operation of an exhibit, tool, machine, or safety system.
Evidence-Based Mechanics Report: Investigate a challenging claim about motion, such as whether a heavier cart always accelerates more; design a controlled test or use reliable data, analyze uncertainty, and present a reasoned conclusion with diagrams and equations.

Learning Assessment

Seat-Belt Reasoning: Explain how Newton’s first law helps account for the motion of a passenger during sudden braking, then connect your explanation to the function of a seat belt without claiming that the belt removes inertia.
Force and Mass Transfer Problem: A loaded cart and an empty cart experience the same net force; predict which accelerates more, calculate a sample case using chosen realistic masses, and explain how your mathematics supports the prediction.
Third-Law Analysis: Choose one interaction from walking, swimming, jumping, or rocket motion; identify the two objects, state the force each exerts on the other, and explain why the pair does not cancel on a single object.
Diagram-to-Equation Challenge: Create a free-body diagram for a box pulled across a rough floor, assign plausible force values, calculate the net force, and determine the acceleration for a stated mass.
Experimental Evaluation: Evaluate a class experiment on Newton’s second law by identifying controlled variables, sources of uncertainty, and one improvement that would make the evidence more convincing.
Model Limits: Explain one everyday situation in which Newtonian mechanics is an excellent model and contrast it with one extreme situation where relativity or quantum mechanics would be required.

Evidence of Learning

Knowledge: You can state the three laws in your own words and accurately use the concepts of force, mass, inertia, acceleration, net force, friction, weight, and normal force.
Representation skills: You can draw and interpret free-body diagrams, combine force vectors in simple one-dimensional cases, and connect diagrams to equations.
Calculation skills: You can use $F_{net} = m a$ and $W = m g$ with correct units and explain the direction of acceleration.
Reasoning skills: You can distinguish balanced forces from third-law pairs and correct common misconceptions about force and motion.
Practical skills: You can plan a safe investigation, collect and organize data, identify variables, and evaluate sources of uncertainty.
Products: Your evidence may include diagrams, laboratory notes, graphs, calculations, posters, photos, videos, interviews, or engineering prototypes.
Transfer: You can apply Newton’s laws to unfamiliar examples in transport, sports, technology, safety, and spaceflight and explain where the Newtonian model has limits.

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