Welcome to Newton's Laws. The forces met so far were drawn on free-body diagrams in Weight, Springs & Friction, and added up and balanced in Resultant Force & Equilibrium. This topic asks the question those two led up to: what does a force do to a body's motion? Newton answered it with three laws of motion. This page gives the first. It starts with the thought experiment that convinced Galileo that motion needs no force to keep it going, states the law, and then looks at the property the law describes, inertia, and at what measures it. The last part uses the law one direction at a time, which is how the papers have tested it.
Only one question in the four papers so far has tested the first law on its own: March 2026 Q44, a hard item among the last five questions of the paper, worked through below. It needs almost no arithmetic, only a clear view of which forces act and which way they point. The law also sits inside many other questions. Every question about a body "moving uniformly" starts from it, and the next page, The Second Law: F = ma, builds straight on it: the first law says that a net force is what changes a velocity, and the second says by how much.
Galileo's ideal ramp
For about two thousand years the usual answer to "what keeps a body moving?" came from Aristotle: a force. Stop pushing a cart and it stops, so motion seemed to need a push all the time. Galileo, around 1600, suspected that the stopping was the work of friction, and that a body left alone would not stop at all. He could not remove friction completely, so he reasoned from a pattern in real experiments to the ideal case.
Take two ramps facing each other, joined at the bottom. Release a ball from rest partway up the first. It rolls down, then up the second ramp, and on smooth ramps it climbs almost back to the height it started from. The smoother the ramps, the closer it comes, so Galileo concluded that on perfectly smooth ramps it would reach exactly its starting height.
Now make the second ramp less steep. The ball still climbs back to the same height, but it has to roll further along the ramp to get there. Make the ramp gentler again and it rolls further still. Finally, make the second ramp level. Now the ball can never climb back to its starting height, so it never reaches a point where it stops, and it rolls on for ever at a steady speed.
Galileo's ideal ramps. Whatever the slope of the second ramp, the ball climbs back to its starting height (dashed); the gentler the slope, the further it rolls to get there. On a level track it can never get back up to that height, so it never stops.
So on a level, perfectly smooth surface, nothing changes the ball's motion, and it keeps going without any push. What stops a real ball is friction, a force acting against its motion. This is called an ideal experiment, or thought experiment: no ramp is perfectly smooth, and no level track goes on for ever, so it cannot be carried out as described. It takes a pattern seen in real experiments to its limit. Soon afterwards Descartes added the other half: a moving body left alone keeps not only its speed but also its direction, so it moves in a straight line.
Try it! · Check-in question
In Galileo's ideal experiment, the second ramp is perfectly smooth and is made less and less steep, until at last it is level. What did he conclude the ball does on the level ramp?
On every slope the ball climbs back to its starting height, and the gentler the slope, the further it rolls to get there. On a level ramp it never gets back up to that height, so nothing makes it stop, and with no friction nothing slows it either. The answer is B. A invents a rule about equal distances; the pattern Galileo saw was equal heights. C is the old view that motion needs a push. Slowing down is a change of motion, and on a perfectly smooth level track there is no force to cause it. D treats the slope as what keeps the ball moving, but the first ramp only speeds the ball up; at the bottom it is already moving and needs nothing more.
Newton's first law
Newton put Galileo's and Descartes' ideas together as the first of his three laws of motion, published in 1687. It covers the two states a body keeps by itself: rest, and moving at a steady speed in a straight line, which the Speed & Velocity page called uniform linear motion. In both, the velocity is constant.
Newton's first law. Every body stays at rest, or keeps moving in a straight line at a constant speed, unless a net force acts on it and makes it change that state. It is also called the law of inertia.
Read the law in two halves. First, a body keeps its velocity by itself, so no force is needed to keep it moving. Second, a net force is what changes a velocity, and a velocity changes whenever the speed changes, or the direction, or both. So a body speeding up, slowing down or going round a bend at a steady speed must have a net force on it.
Notice that the law speaks of the net force, the resultant of the Resultant Force & Equilibrium topic. A body can have several forces on it and still keep its velocity, if they balance. A car cruising along a straight road at a steady speed has a driving force forwards and friction and air resistance backwards, and its velocity does not change because they cancel. So "a force acts on the body" does not mean "its motion changes". The law runs both ways: zero net force means a constant velocity, and a constant velocity means zero net force. The Equilibrium: Zero Net Force page used the second direction every time it said that a body moving uniformly is in equilibrium.
Net force and velocity. Net force zero ⇔ velocity constant (at rest, or a steady speed in a straight line). Velocity changing, in size or in direction ⇔ net force not zero. Forces can act on a body without changing its motion, as long as they balance.
A law about an ideal. No real body is free of all forces: gravity acts everywhere near the Earth, and there is always some friction or air. So the first law cannot be checked by watching a body with no forces on it. It was reached as Galileo reached his conclusion, by reasoning from real experiments to the ideal case, and it is trusted because everything that follows from it agrees with measurement. What you can watch are bodies whose forces balance, and they do keep their velocity.
Try it! · Check-in question
By Newton's first law, which of these bodies must have a net force acting on it?
A net force is needed whenever the velocity changes, and velocity has a direction as well as a size. The car's speed is steady, but its direction keeps turning, so its velocity changes and a net force must act on it. The answer is D. A is moving, but at a constant velocity, so the forces on it balance: the cable's pull equals the weight of the lift and its load. B is at rest and stays at rest, because gravity and the desk's push balance. C moves downwards under gravity, but its velocity is constant, so air resistance has grown to match its weight and the net force is zero. Whether a body moves and whether a net force acts are different questions: the first law links a net force to a change in velocity, not to the velocity itself.
Inertia
The first law describes a property that every body has: left to itself, it keeps its velocity. A body at rest stays at rest, and a moving body keeps moving at the same speed in the same direction. This tendency to keep its state of motion, and so to resist any change in it, is called inertia. That is why the first law is also called the law of inertia.
Inertia. Inertia is the tendency of a body to keep its state of motion: to stay at rest if it is at rest, and to keep moving at the same speed in the same direction if it is moving. Every body has inertia at all times, whether it is moving or not and whatever forces act on it.
Inertia explains many everyday effects, and they all work the same way. A force acts on one body, or one part of a body, and changes its motion. Another part, which the force does not reach, carries on as before.
Put a card on top of a glass and a coin on the card, then flick the card away sharply. The card shoots off, but the coin drops into the glass. The flick acts on the card. The friction on the coin is small and lasts only a moment, so the coin gains hardly any sideways velocity: by its inertia it stays almost where it was, and gravity pulls it into the glass.
Stand in a bus that pulls away suddenly, and you tip backwards. Friction from the floor drags your feet forwards with the bus. Nothing pushes the upper part of your body forwards at that moment, so by its inertia it stays where it was, while your feet move off beneath it.
Inertia is not a force. A force needs two objects, an agent and a receiver, as the What a Force Is page showed. Inertia has no agent: it is a property of the body itself. So say "because of its inertia, the coin stays where it is", never "the force of inertia" or "the coin is acted on by inertia". Statement questions plant exactly this slip.
Try it! · Check-in question
A bus moving along a straight road brakes suddenly, and a standing passenger lurches forwards. What is the best explanation?
Before the brakes go on, the passenger moves forwards with the bus. Braking slows the bus, and friction from the floor slows the passenger's feet along with it. No force acts that quickly on the upper body, so by its inertia it carries on forwards, and the passenger tips. The answer is C. A treats inertia as a force; it has no agent, and nothing pushes the passenger forwards. B gets the floor's force the wrong way round: the friction on the feet points backwards, which is why the feet slow down. D is wrong twice: the braking force acts on the bus's wheels, not on the passenger, and it points backwards, against the motion.
Mass measures inertia
Do all bodies have the same inertia? Push an empty supermarket trolley and a fully loaded one with the same force for the same short time. The empty one sets off quickly; the loaded one gains much less speed. Stopping them works the same way: with the same force, the loaded trolley takes longer to stop. The more mass a body has, the less a given force changes its velocity in a given time, so the harder it is to change its state of motion. Mass is the measure of inertia. The next page makes this exact.
Mass and inertia. The inertia of a body depends only on its mass. The larger the mass, the greater the inertia, and the harder it is to change the body's velocity. Its speed, whether it is moving, where it is and which forces act on it make no difference.
Each part of that last sentence answers a common mistake. A fast lorry takes longer to stop than a slow one, which tempts people to say that speed adds inertia. Go back to the trolleys: the same braking force takes velocity away from the same lorry at the same rate, whatever its speed. The fast lorry takes longer only because it has more velocity to lose. The rate, which is what inertia is about, depends on the mass alone.
A parked car has exactly as much inertia as the same car moving: inertia is what makes it hard to start as well as what makes it hard to stop. And on the Moon a lorry weighs only about a sixth of its weight on the Earth, because the Moon's gravity is weaker, but its mass is the same. A given net force would change its velocity just as slowly as on the Earth. Inertia goes with mass, not with weight, which the Gravity & Weight page showed are different quantities.
Try it! · Check-in question
Which statement about inertia is correct?
Mass is the only measure of inertia. Loading the lorry adds mass, so it gains inertia and becomes harder both to start and to stop. The answer is A. B forgets that a parked car resists being set moving, and that resistance is inertia too. C confuses inertia with the time it takes to stop. The faster car has more velocity to lose, but the same braking force slows it at the same rate, because its mass is unchanged. D mixes up mass and weight: her weight is smaller on the Moon, but her mass, and so her inertia, is the same.
One direction at a time
Force and velocity are both vectors, and the Adding & Resolving Forces page showed how to split a vector into two perpendicular parts and handle each part on its own. The first law can be split in the same way. Take the horizontal and vertical directions. If no force acts horizontally, nothing can change the horizontal part of the velocity, whatever happens vertically. So the horizontal velocity stays exactly what it was, while any vertical force changes only the vertical velocity.
Take a crate dropped from a plane flying level at a constant velocity, and ignore air resistance. Before it is released, the crate moves with the plane, so it has the plane's horizontal velocity. After release, the only force on it is gravity, which is vertical. Horizontally there is no force, so by the first law the crate's horizontal velocity stays equal to the plane's: it keeps up with the plane and stays directly below it all the way down. Vertically, gravity makes it fall faster and faster, as in free fall. Seen from the ground, the crate follows a curve; seen from the plane, it falls straight down, which is the reference-frame idea of the Describing Motion topic. A parcel dropped from the window of a train moving steadily does the same: it keeps the train's forward velocity and stays level with the window as it falls.
A crate dropped from a plane flying level at a constant velocity, drawn at equal time steps, with air resistance ignored. Gravity acts only downwards, so the crate keeps the plane's horizontal velocity (blue, the same at each step) and stays directly below the plane, while its vertical velocity (red) grows. From the ground its path is a curve; from the plane it falls straight down.
The first law along one direction. If the net force along a direction is zero, the velocity along that direction never changes. A body with no horizontal force keeps its horizontal velocity exactly: if it started with none, it moves only straight up or down; if it started with some, it keeps all of it.
Try it! · Check-in question
A train moves along a straight, level track at a constant velocity. A passenger standing in the aisle throws a ball straight up, as she sees it, and keeps her hand where it is. Ignoring air resistance, where does the ball come down?
When it leaves her hand, the ball already has the train's forward velocity. In the air the only force on it is gravity, which is vertical, so its forward velocity stays equal to the train's and it keeps level with her hand the whole time. It comes straight back down into her hand, so the answer is A. B and D imagine that the ball loses the train's forward velocity once it leaves her hand; nothing acts horizontally to take it away, so it keeps it, at any steady train speed. C has the ball moving forwards faster than the train, which would need a forward force on it in the air, and there is none.
A ball on a sliding wedge
The papers have tested the first law with a question that looks harder than it is. The whole method is to list the forces on the ball, see which way each one points, and apply the first law to the direction in which nothing acts.
Worked example · inertia along one direction (March 2026, Q44)
As shown in the figure, a smooth wedge M with a horizontal top surface is placed on a fixed incline plane. A smooth ball m is placed on the wedge. When the wedge is released from rest, before the ball hits the slope, the ball's trajectory is ( ).
A. Irregular curve
B. Straight line along the slope downwards
C. Parabola
D. Straight line vertically downwards
The set-up of March 2026 Q44: a smooth wedge with a horizontal top on a fixed incline, and a smooth ball on the top, all released from rest.
Step 1: list the forces on the ball. Gravity, mg, points vertically down. The only thing the ball touches is the top of the wedge. That surface is smooth, so it gives a normal force only, and a normal force is perpendicular to the surface. The top is horizontal, so its push N points vertically up. Both forces on the ball are vertical: there is no horizontal force on it at all.
Step 2: apply the first law horizontally. The ball starts at rest, so its horizontal velocity is zero. With no horizontal force, it stays zero. The ball never moves sideways.
Step 3: vertically, the forces do not balance once the wedge moves. As the wedge slides down the slope its top sinks, and the ball sinks with it, staying on the top. The ball keeps sinking until the corner where the top meets the slope reaches it, and there it meets the slope. All that time it moves only downwards, so its path is a straight vertical line, and the answer is D.
B is the tempting option: it lets the ball ride along with the wedge. But moving down the slope means moving sideways as well as down, and that needs a horizontal force. Only friction from the top could supply one, and the top is smooth. C, a parabola, is the path of a body that starts with a horizontal velocity, like the crate from the plane; this ball starts with none and gains none. A has nothing behind it: forces that are all vertical cannot bend the path sideways.
The question does not say whether the fixed incline is smooth. That makes no difference: however fast the wedge slides, the ball feels only vertical forces.
Left: at release, the only forces on the ball are its weight mg and the push N from the smooth horizontal top, and both are vertical. Right: the moment the ball reaches the slope. The wedge has slid down the slope, but the ball has only sunk with the top, straight down, and it meets the slope at the wedge's corner, directly below where it started.
Compare the ball with the crate from the plane. Both follow the same rule: no horizontal force, so no change in horizontal velocity. The crate started with the plane's horizontal velocity and kept it, so it followed a curve. The ball started with none and kept none, so it falls straight down. When a question asks for a path, first find the starting velocity, then ask along which directions a force acts.
Exam wording. "Smooth" (光滑 in Chinese papers) means frictionless, so a smooth surface can only push at right angles to itself. "Trajectory" (轨迹) is the path the body follows. Inertia is 惯性, Newton's first law is 牛顿第一定律, also called 惯性定律 (the law of inertia), and Galileo's ideal ramp is his 理想斜面实验, his ideal-incline experiment.
Try it! · Check-in question
A smooth puck rests on the smooth, level floor of a van that is standing still. The van suddenly pulls away forwards. Until the puck reaches the back of the van, how does it move relative to the road?
The forces on the puck are gravity and the floor's push, and a smooth level floor can push only straight up, so both are vertical. With no horizontal force, the puck's horizontal velocity stays at its starting value, zero: it stays where it is on the road while the van moves forwards beneath it. The answer is D. A and B both need a forward force on the puck, and only friction could supply one; the floor is smooth. C confuses the two points of view. Seen from inside the van the puck slides backwards, but that is the van moving forwards, not the puck moving backwards over the road.
Statement questions on the first law
The papers test ideas like these with statement questions: four statements about force and motion, and you pick the correct one, or the incorrect one. Test each statement against four facts.
1
Force and motion. No force is needed to keep a body moving. A net force is needed to change its velocity: to speed it up, slow it down or turn it.
2
Net force, not force. Forces can act while the velocity stays constant, as long as they balance. "No net force" is not "no forces".
3
Inertia. Every body has it, at all times. Mass alone measures it, not speed and not weight. It is not a force.
4
One direction at a time. Along a direction with no net force, the velocity never changes.
As always, read the stem again before you choose: does it ask for the correct statement or the incorrect one?
Try it! · Check-in question
Which statement about force and motion is correct?
A change in velocity, in size or in direction, is exactly what a net force causes, and nothing else can cause it. So the answer is C. A confuses zero net force with no forces: a car cruising steadily has a driving force and resistance on it, and they balance. B is the old view that motion needs a push. With zero net force a body keeps its velocity, so it carries on at the speed it had. D also treats force as what keeps a body moving; a body moving at any steady speed in a straight line needs zero net force.
You will meet this again. The first law settles one option in a question that has come up three times, as December 2025 Q46, January 2026 Q46 and March 2026 Q47: a wire pulled at a constant velocity along rails in a magnetic field. One option says that once the wire is up to speed, the pull can be removed and the wire will carry on at a constant velocity. That is false. While the wire moves, the magnetic field pushes back on it, and only the pull balances that push. Remove the pull and the magnetic force is left unbalanced, so the wire slows down. A later topic explains where that force comes from; the first law is all you need to reject the option.
Your turn! · Practice questions
Practice · Question 1
A hammer head has worked loose on its wooden handle. Holding the hammer head-up, a carpenter bangs the bottom of the handle hard on the floor, and the head slides further down onto the handle. Why?
Head and handle move down together. When the handle hits the floor, the floor's upward push stops it almost at once. The head is only loosely joined to the handle, so that push hardly reaches it, and by its inertia it keeps moving down, sliding further onto the handle. The answer is B. A misses the point: gravity pulls on the head all the time, yet the head does not slide while the hammer is simply held; what makes it slide is the sudden stop. C gets the direction wrong: a push passed up from the handle would point upwards, which would loosen the head, not tighten it. D treats inertia as a force; inertia is a property of each body itself and has no agent.
Practice · Question 2
Which of these has the greatest inertia?
Inertia depends on mass alone, so the 1500 kg car has the most, although it is not moving at all. The answer is D. A is by far the fastest but has the smallest mass, so it has the least inertia; its speed only means it has a lot of velocity to lose. C may look right because a fast, heavy motorbike is hard to stop, but its mass, 200 kg, is far below the car's. B has a smaller mass still, and its speed makes no difference either.
Practice · Question 3
A puck tied to a string slides on smooth, level ice in a horizontal circle at a steady speed, around the peg the string is tied to. Suddenly the string breaks. Seen from above, how does the puck move after that?
While the string pulled, it kept turning the puck's velocity towards the peg. Once it breaks, the only forces left are gravity and the push of the ice, which are vertical and balance. With no horizontal force, the puck keeps the velocity it had at that instant, in size and in direction: it moves in a straight line along the tangent to the circle at a steady speed. The answer is A. B imagines that the puck remembers the circle, but turning needs a force towards the centre, and that force has gone. C has the puck flung outwards; nothing pushes it outwards, and at the instant the string breaks its velocity is along the tangent, not along the radius. D still needs a sideways force to keep bending the path, and there is none.
Practice · Question 4
A puck slides due east at 5 m/s across smooth, level ice. A steady force pointing due north then starts to act on it. Which statement about the puck's motion after that is correct?
Treat the two directions separately. Nothing acts east or west, so by the first law the eastward velocity stays 5 m/s. Northwards there is a net force, so the northward velocity changes: it grows from zero, and the path bends more and more towards the north. The answer is C. A would need the eastward velocity to vanish at once, which needs a force towards the west, and there is none. B also takes eastward velocity away without a westward force. D says the force does nothing, but a net force always changes the velocity along its own direction; here the change is northwards.
Practice · Question 5
Which of the following statements is incorrect?
The stem asks for the incorrect statement. B is the old view that motion needs a force. By the first law a body keeps moving with no force at all, and an unbalanced force along its motion would speed it up, not just keep it going. So B is false, and the answer is B. A is true: a book on a table has gravity and the table's push on it, and they balance. C is true, because mass is the measure of inertia. D is true when the direction changes: a car going round a bend at a steady speed has a net force on it, because its velocity keeps changing direction.
Things to remember
Concept
What to know
Galileo's ideal ramp
On smooth ramps the ball climbs back to its starting height, however gentle the slope. On a level track it never can, so it rolls on for ever. Motion needs no force to keep it going; friction is what stops real bodies.
Newton's first law
A body stays at rest, or keeps moving in a straight line at a constant speed, unless a net force changes that state. Also called the law of inertia (牛顿第一定律, 惯性定律).
Net force and velocity
Net force zero ⇔ constant velocity. A change of speed or of direction needs a net force. Forces can act without changing the motion, as long as they balance.
Inertia
A body's tendency to keep its state of motion (惯性). Every body has it, at all times. It is not a force: say "because of its inertia", never "the force of inertia".
Measure of inertia
Mass, and only mass. Not speed, not whether the body is moving, not its weight or where it is.
One direction at a time
With no net force along a direction, the velocity along it never changes. No horizontal force means the horizontal velocity stays what it was.
Released from a moving body
It keeps the carrier's horizontal velocity: a crate stays below the plane, a ball thrown up in a steady train lands back in the hand.
Smooth surfaces
A smooth surface pushes only at right angles to itself, so a smooth horizontal top gives no horizontal force. March 2026 Q44: the ball on the sliding wedge falls straight down (D).
Statement traps
"No forces" for "zero net force"; motion needing a force; faster meaning more inertia; "acted on by inertia". Check whether the stem asks for the correct or the incorrect statement.
