Newton’s Laws · Chapter 1
The First Law: Inertia
Slide a book across a table and it stops. So it seems obvious that a moving thing needs a push to keep going, and for two thousand years most people thought so. Galileo saw what was hiding in plain sight: friction. Take friction away and a moving thing keeps going, straight ahead at the same speed, forever. Here you can roll a ball between Galileo’s two ramps, coast a probe through deep space, and pull a tablecloth out from under the dishes. By the end you will see the first law everywhere, from seat belts to the spacecraft that is now farther from home than anything people have ever built.
Galileo’s ramps
No friction at all: nothing on the track can slow the ball down.
Live numbers
Missions
What you’re seeing
Two ramps. A ball rolls down the left ramp, across a short flat, and up the right ramp. The dashed gold line is the height it started from. Each time the ball turns around, a pink mark shows how high it got. With no friction, every mark sits on the gold line.
The right ramp. Drag its gold handle, or use the slider, to make it gentler. The ball still climbs to the same height, but it has to roll farther to get there. Make it flat and there is no height to reach, so the ball never turns around.
The graph. The green line is the ball’s speed. Going downhill it rises, going uphill it drops. On a flat, frictionless track it is a perfectly level line: the speed does not change at all.
The energy bar. Blue is energy stored in height, green is energy of motion, red is energy turned into heat by friction. Without friction the bar never turns red; blue and green just trade places.
The first law
Newton’s first law says that an object keeps doing what it is doing unless a force makes it change. If it is still, it stays still. If it is moving, it keeps moving at the same speed in the same direction. Only a net force, the total of all the forces on it, can change that.
Velocity means speed and direction together. So a car going around a bend at a steady 50 km/h is changing its velocity, and that needs a force (Chapter 6 is all about that). A puck sliding straight across ice at a steady 5 m/s has no net force on it, even though it is moving fast.
This stubbornness, the way things keep their motion, is called inertia. The amount of inertia is measured by mass. A 4,000 kg probe has four times the inertia of a 1,000 kg probe: the same push changes its speed only a quarter as much. Mass is measured in kilograms, and unlike weight, it is the same on Earth, on the Moon or in deep space.
Staying still and moving steadily in a straight line are the same thing to physics: both mean the net force is zero.
A force is not what keeps something moving. A force is what starts it, stops it, speeds it up, slows it down or turns it.
The more mass something has, the harder it is to change its motion, in any direction.
Coasting in deep space
Far from planets and stars there is no air and no ground: nothing to rub against. Fly this probe with short thruster bursts. Each tap pushes with 500 N for half a second. Watch the gold dots: the probe drops one every second. When nothing pushes, they line up straight and evenly spaced.
The probe
Missions
Galileo’s ramps
Galileo Galilei rolled balls down ramps in the early 1600s, and he also reasoned about ramps he could not build. A ball let go on one ramp rolls up a facing ramp to almost the height it started from. The smoother the surfaces, the closer it gets. So, with no friction at all, it would reach exactly the same height.
Now make the second ramp gentler. To reach the same height, the ball has to roll farther. Gentler still, and it rolls farther still. Now make the second ramp flat. There is no height to climb back to, so the ball has no reason ever to stop. Without friction, it would roll on at the same speed forever. That is the first law, found by pushing an everyday experiment to its limit.
The ball starts 0.50 m up. Its height energy per kilogram is g h = 9.81 m/s² × 0.50 m = 4.90 J/kg. A rolling ball also spins, and a solid ball’s spin takes 2/7 of its motion energy, so (7/5) × ½v² = 4.90 J/kg and
That is the level line on the graph when the right side is flat. A block sliding down without friction would not spin and would reach √(2g h) = 3.13 m/s. Either way, on a flat, frictionless track that speed never changes.
Friction, the hidden force
On Earth almost everything that moves rubs against something: the ground, the air, its own axle. Friction pushes backward on moving things, so they slow down and stop. Because friction is everywhere and invisible, it is easy to think that stopping is just what moving things do. It is not. Stopping is what a backward force does.
In the ramp simulation, carpet pushes back with 5% of the ball’s weight, wood 1.5% and ice 0.4%. On the flat, the ball then loses speed at a steady rate: on carpet 0.35 m/s every second, on ice only 0.028 m/s. From 2.65 m/s, that is 10 m of carpet but about 125 m of ice. Less friction, longer roll. No friction, endless roll.
“A moving thing needs a force to keep it moving.” No: it needs a force to keep it moving only when something else is pushing back, such as friction or air drag. A bicycle on a flat road needs you to pedal because the air and the tires push back. If you match those forces exactly, the net force is zero and you cruise at a steady speed. Your pedaling is not what keeps you going; it cancels the forces that would stop you.
Inertia in everyday life
Each of these is the first law in disguise. Press the buttons, and watch which things keep doing what they were doing.
The dishes are at rest. Friction from the cloth can only move them while the cloth is still under them.
You can try this one at home with a plastic cup, a playing card and a coin.
50 km/h, braking hard at 0.7 g, about what skidding tires on dry concrete give.
The train goes at a steady 30 m/s (108 km/h). The ball is let go 1.5 m above the floor.
The tablecloth. Friction between cloth and dishes is a real force, but a force needs time to change motion. Yank the cloth fast enough and it is gone before the dishes have picked up much speed. (Practice with plastic cups, not your family’s plates.)
The coin. Lay a playing card on a plastic cup, put a coin in the middle, and flick the card sideways with your finger. The card shoots away, and the coin stays put and drops into the cup. A slow push drags the coin along. It is a safe experiment for any kitchen table.
The braking car. When a car brakes, the brakes and the tires slow the car, not you. Your body keeps moving forward at the speed you had until something pushes back on you. A seat belt is that something, pushing on your strong hips and chest and spreading the stop over the whole braking distance.
The train. On a smooth train going straight at a steady speed, a dropped ball falls straight down at your feet. It was already moving forward at 30 m/s with you, and nothing took that away. From the platform, the same fall is a curve.
A car going 50 km/h (13.9 m/s) brakes at 0.7 g = 6.9 m/s². It stops in 13.9 ÷ 6.9 = 2.0 s, after 13.9² ÷ (2 × 6.9) = 14 m. An unbelted passenger keeps going at 13.9 m/s. The car falls behind the passenger by ½ × 6.9 × t², so a 45 cm gap to the dashboard closes after √(2 × 0.45 ÷ 6.9) = 0.36 s, when the passenger is moving 6.9 × 0.36 = 2.5 m/s (9 km/h) faster than the car. In a crash, the car stops in a fraction of a second, and an unbelted person hits the inside of the car at nearly the full speed.
That is why belts matter. The U.S. National Highway Traffic Safety Administration estimates that seat belts saved 14,955 lives in 2017, and that for people in the front seat of a passenger car, buckling up reduces the risk of a fatal injury by 45%.
Moving or not? Inertial frames
On a smooth plane at cruising speed, you can pour a drink, toss a ball and walk down the aisle as if you were standing still on the ground. Everything in the cabin is already moving with you, and keeps moving. If the windows were covered, no experiment inside a smoothly moving cabin could tell you how fast you were going.
A place where the first law works, where things at rest stay at rest and moving things go straight, is called an inertial frame of reference. Any frame moving at a steady velocity relative to an inertial frame is inertial too. A train speeding up, braking or turning is not: there, a ball on the floor starts rolling with no force pushing it. That is inertia showing up as a lurch.
Voyager: the first law in space
NASA’s Voyager 1 was launched on September 5, 1977. It flew past Jupiter in 1979 and Saturn in 1980, and in 2012 it became the first spacecraft to reach interstellar space. It has no engine pushing it along; its small thrusters only keep its antenna pointed at Earth. It just coasts, at nearly 38,000 mph (61,000 km/h). The Sun’s gravity still tugs back on it, but that far away the tug is tiny. On November 18, 2026, NASA expects Voyager 1 to be one light-day from Earth: about 26 billion kilometers, so far that its radio signals take a whole day to reach us.
61,000 km/h ÷ 3,600 s/h = 16.9 km/s. A year is 365.25 × 24 × 3,600 = 31,557,600 s, so in one year Voyager 1 coasts
An AU is the average distance from Earth to the Sun, 149,597,870.7 km. NASA’s own figure for Voyager 1 is about 3.6 AU per year, the same answer. No fuel was burned for any of it.
From Aristotle to Newton
Aristotle, in Greece in the 300s BC, taught that an object on Earth moves only as long as something keeps pushing it. Stop pushing, and it settles back to rest, which he took to be its natural state. It matches what you see every day, because friction is everywhere, and it was taught for nearly two thousand years.
Galileo Galilei (1564–1642) argued, in books published in 1632 and 1638, that a ball on a smooth, level surface would keep rolling unless something slowed it. Friction and air, not the nature of things, bring moving objects to rest.
René Descartes wrote in his Principles of Philosophy (1644) that a body keeps its motion unless something changes it, and that motion on its own goes in a straight line.
Isaac Newton made it the first of his three laws of motion in the Principia, published in London in 1687, and used it with the other two to explain the motion of everything from cannonballs to the Moon.
Lex I. Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
Law I. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impress’d thereon.
Isaac Newton, Philosophiæ Naturalis Principia Mathematica (London, 1687), Axioms, or Laws of Motion. English by Andrew Motte, The Mathematical Principles of Natural Philosophy (London, 1729). A “right line” is a straight line.Right after the law, Newton gives examples. The first is about air resistance and gravity, the forces that hide the first law from us every day:
Projectilia perseverant in motibus suis nisi quatenus a resistentia aeris retardantur & vi gravitatis impelluntur deorsum.
Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity.
Newton, Principia, after Law I (1687); Motte’s translation (1729).Where you see it
- Seat belts, airbags and headrests all work on inertia: they push on you so that you slow down, or speed up, together with the car. The Brakes lesson of the Cars course shows how a car makes the force that stops it.
- Spacecraft coast most of the way. Rocket engines burn for minutes; the trip to the Moon is mostly coasting, steered by gravity. Try it in Orbit Lab and Rocket Builder.
- Hockey and curling: on smooth ice, a puck or a stone keeps going a long way after one push, because ice friction is small.
- Shaking off water: when a dog shakes itself or you shake a wet umbrella, the drops keep going when the fur or the umbrella swings back.
- Loads on a truck slide forward when it brakes, which is why cargo is strapped down.
How the simulation works
The ramps. The track is two straight ramps (the left one at 30°) joined to a 0.6 m flat by curves of 0.3 m radius, so the ball never hits a sharp corner. The ball is a solid ball rolling without slipping, so its motion energy is (7/5) × ½mv². Along the track it obeys
where θ is the slope, κ the curvature of the track (zero on the straight parts) and C the rolling resistance, as a fraction of the push between ball and track. The surfaces use illustrative values of C: carpet 0.05, wood 0.015, ice 0.004. Real values depend on the ball. When the ball stops where the slope is gentler than the resistance can hold, it stays put. The equation is stepped forward 1,000 times per simulated second with the fourth-order Runge–Kutta method, with g = 9.80665 m/s², the standard value.
Checks. With no friction, released from 0.500 m, the ball turned around at 0.50000 m on right ramps of 60°, 45°, 30°, 15°, 5° and 2°, after rolling 0.40, 0.58, 0.92, 1.89, 5.72 and 14.32 m up them. Its energy stayed constant to 3 parts in a million. Its speed on the flat was 2.64665 m/s, matching √(10gh/7), and did not change in the 12th decimal place over 100 simulated seconds. With friction, the stopping distances on the flat matched the formula 7v²/(10 C g) to better than 0.1%, and energy plus heat stayed constant to 0.02%. Run backward for 3 seconds, the ball came back to its starting point within a billionth of a meter.
The probe feels no friction unless you switch it on (then it slows at 0.29 m/s² until it stops). In tests, a probe coasting for 100 s at 0.3 m/s right and 0.2 m/s down ended exactly 30 m right and 20 m down, and a 0.5 s, 500 N burst changed a 1,000 kg probe’s speed by exactly 0.25 m/s and a 4,000 kg probe’s by 0.0625 m/s. The demos use the same laws: the cloth and the card pull with friction (μ = 0.3, a typical value) only while they are under the dishes or the coin; the car brakes at 0.7 g; the train goes at a steady 30 m/s.
Check yourself
A puck slides across perfectly frictionless ice at 5 m/s. Nothing else touches it. What happens next?
Show the answer
With no net force, its velocity cannot change: same speed, same direction. Real pucks stop because real ice has a little friction.
A ball rolling across a carpet slows down and stops. Why?
Show the answer
A moving object does not carry a supply of force. Friction is an outside force pushing backward, and it is what takes the speed away.
The same thruster burst is fired on a 1,000 kg probe and on a 4,000 kg probe. Which changes speed more?
Show the answer
More mass means more inertia. In the simulation one tap gives the light probe 0.25 m/s and the heavy one 0.0625 m/s.
You are on a smooth train going straight at a steady 100 km/h. You toss a coin straight up. Where does it land?
Show the answer
The coin was already moving forward at 100 km/h with you and the train, and nothing takes that away (in a closed carriage the air moves with you too). A steadily moving train is an inertial frame.
In Galileo’s ramps with no friction, you make the second ramp much gentler. The ball…
Show the answer
It always gets back to its starting height. Make the ramp flat and it can never get there, so it rolls on forever.
Why do the dishes stay behind in the tablecloth trick?
Show the answer
Friction does pull the dishes, but only while the cloth is under them. A quick yank lasts about a tenth of a second, so they move only a few centimeters.
Sources
- OpenStax, University Physics Volume 1, 5.2 Newton’s First Law (inertia, inertial frames)
- OpenStax, University Physics Volume 1, 6.2 Friction (rubber on dry concrete, μk ≈ 0.7)
- Isaac Newton, Philosophiæ Naturalis Principia Mathematica, London, 1687 (scan at the Internet Archive: Axiomata, sive Leges Motus)
- The Mathematical Principles of Natural Philosophy, translated by Andrew Motte, 1729: Axioms, or Laws of Motion (Wikisource)
- NASA JPL, Voyager Fast Facts (launch, interstellar space, 3.6 AU per year)
- NASA Science, Voyager 1: What Is a Light-Day? (speed; one light-day on November 18, 2026)
- NHTSA, Seat Belts (lives saved in 2017; 45% lower risk of fatal injury)
- NIST Guide to the SI, Appendix B.8 (standard acceleration of gravity, 9.80665 m/s², exact)