Newton's Three Laws of Motion · Grade 12 Science

Newton's Three Laws of Motion

Learning goals

• I can state Newton's three laws of motion and explain inertia as an object's resistance to changes in motion.
• I can apply Newton's second law (F = ma) to solve for net force, mass, or acceleration.
• I can identify action-reaction force pairs and explain why the two forces act on different objects.

Readings for this unit

• The force on the box is not the force on the floor

Newton’s laws describe a powerful model for ordinary macroscopic motion in inertial frames. A force is an interaction that contributes to acceleration through the net-force account. Their range is not literally every physical situation: relativistic speeds, quantum-scale evidence and rotating frames need additional models. Within their useful range, identify the object, interactions, mass and coordinate directions to predict how its velocity changes.

Newton's first law, the law of inertia, states that an object keeps doing whatever it is already doing — sitting still or gliding at constant velocity in a straight line — unless a nonzero net force acts on it. Inertia is simply an object's built-in resistance to any change in its motion, and its mass is the direct measure of that resistance. This law overturned a 2,000-year-old belief, going back to Aristotle, that motion needs a continuous push to keep going. The truth is the reverse: a rolling ball slows only because friction and air resistance push back on it. Remove those forces, as in deep space, and the ball glides on forever with no engine at all.

Newton's second law turns that idea into an equation: ΣF = ma, the net force on an object equals its mass times its acceleration. Read carefully, it says two intuitive things at once. First, for a given mass, a larger net force produces a larger acceleration — push harder and it speeds up faster. Second, for a given net force, a larger mass produces a smaller acceleration — that is inertia again. The Greek letter Σ (sigma) means 'sum of,' a crucial reminder that acceleration depends on the *net* force, the single vector left after every push and pull is combined. Force is measured in newtons (N), where one newton accelerates one kilogram at one meter per second squared.

Because it is a vector equation, the second law also tells you the *direction* of the acceleration: an object always accelerates in the same direction as the net force acting on it. Rearranged, the same relationship lets you solve for whatever is unknown — acceleration a = ΣF ÷ m, or mass m = ΣF ÷ a. This one compact formula is the workhorse of the entire unit; nearly every problem you meet, from a sliding crate to an orbiting satellite, comes down to finding the net force and dividing by the mass.

Newton’s third law describes equal-magnitude opposite-direction interaction forces acting on two different bodies. They do not cancel in a free-body diagram of one body. A swimmer pushes water backward and receives a forward force from it. In walking, the foot can push the ground backward while static friction from the ground acts forward on the foot; vertical support is a separate component. Identify the receiving body for every arrow before summing forces.

This third law explains how a rocket accelerates through the vacuum of space, where there is nothing outside to push against. The rocket hurls hot exhaust gas downward, and by the third law that gas pushes the rocket upward with equal force — the action-reaction pair is entirely between the rocket and its own exhaust. From walking to swimming to spaceflight, the three laws work as a team: the first tells you an object's motion only changes when forces are unbalanced, the second tells you exactly how much it changes, and the third reminds you that forces always come in pairs. Learn to read these three ideas together and you can predict the motion of almost anything.

Model check: Action/reaction forces act on different objects, so they do not cancel in one object’s diagram. a=Fnet/m=2 m/s² along the net force.

Newton's Second Law

ΣF = ma

ΣF is the net force in newtons (N); m is mass in kg; a is acceleration in m/s². Rearranges to a = ΣF ÷ m or m = ΣF ÷ a.

The Newton

1 N = 1 kg·m/s²

one newton is the force that accelerates a 1 kg mass at 1 m/s².

Worked examples

Avoid these mistakes

• Action/reaction forces act on different objects, so they do not cancel in one object’s diagram.

Words to know

inertia

The tendency of an object to resist any change in its state of motion; measured by its mass.

Newton's first law

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

Newton's second law

The net force on an object equals its mass times its acceleration: ΣF = ma.

Newton's third law

For every force one object exerts on a second, the second exerts an equal and opposite force back on the first.

newton (N)

The SI unit of force; 1 N is the force that accelerates 1 kg at 1 m/s², so 1 N = 1 kg·m/s².

From Aristotle to the Principia: a 2,000-year correction

For nearly two millennia, the ancient Greek philosopher Aristotle taught that objects have a 'natural' state of rest and that a continuous force is required to keep anything moving — an idea that matches everyday experience, since carts stop when you stop pushing. Galileo Galilei challenged this in the early 1600 s by imagining perfectly smooth surfaces, reasoning that a ball would roll forever if friction could be removed. In 1687 Isaac Newton published his Principia Mathematica, one of the most influential books in the history of science, which gathered these insights into three crisp laws. The first law's radical claim — that constant velocity, not rest, is the natural state when no net force acts — overturned common sense and launched modern physics.

Does motion require a force? The stubborn misconception

The single most common error in introductory physics is believing that a moving object must have a force pushing it in its direction of travel. It feels obvious: stop pedaling and your bike coasts to a halt. But the bike slows because of friction and air resistance pushing backward, not because it 'ran out of force.' A hockey puck on near-frictionless ice glides at nearly constant speed with no forward force at all. Whenever you see something moving steadily in a straight line, the correct conclusion is that the net force on it is zero — the forces are balanced, exactly as they are for an object sitting still.

Momentum and impulse: the deeper form of the second law

Newton originally framed his second law in terms of momentum, p = mv — a kind of 'quantity of motion.' In this form, force is the rate at which momentum changes: F = Δp/Δt, which rearranges to the impulse relationship F·Δt = Δp. This explains why airbags and crumple zones save lives: they stretch out the time Δt over which a crash brings you to a stop, so the same change in momentum happens with a much smaller force on your body. The familiar ΣF = ma is just this deeper law written for the common case where mass stays constant, which is why momentum ideas underlie collisions, rockets, and recoil.

Rockets in a vacuum: the third law at full throttle

A persistent myth says rockets work by 'pushing against the air,' which would make spaceflight impossible. In truth, a rocket obeys Newton's third law: it throws exhaust gas out the back at high speed, and the gas pushes the rocket forward with an equal and opposite force. The Saturn V that carried astronauts to the Moon weighed roughly 2.9 million kilograms fully fueled and produced about 34 million newtons of thrust at liftoff — enough to overcome its enormous weight. Because the action–reaction pair is entirely between the rocket and its own expelled gas, a rocket accelerates just as well in the vacuum of space as in the atmosphere.

In the real world

Every rocket launch is Newton's third law at full power: engines fling exhaust gas downward, and the gas pushes the rocket up — which is why rockets work even in the vacuum of space.

Exit check

A3 kg cart has 6N net force. Find acceleration.