What is inertia?

Everything that has mass is stubborn about its motion. If it is still, it stays still. If it is moving, it keeps going at the same speed in the same straight line. That stubbornness is called inertia, and it is Newton's first law (NewtonClear).

Mass is the measure of inertia. Its SI unit is the kilogram (kg). Give two carts the same push and the one with twice the mass gains speed half as fast: a = F ÷ m. Turn that round and you have a way to measure mass without gravity at all: m = F ÷ a. A 2 kg cart pulled with 4 N speeds up at 2 m/s²; a 1 kg cart at 4 m/s².

Mass is not weight. Weight is the pull of gravity on a mass, W = m g, in newtons: about 9.8 N for every kilogram on Earth, only 1.6 N on the Moon. Your mass, and your inertia, are the same everywhere (see Chapter 4).

Inertia is behind two party tricks. Flick a card out from under a coin and the coin drops into the glass. Whip a smooth cloth off a table and the plates stay put. Friction does drag the object, but only for a split second, and its inertia means it hardly gets going. Speed is the secret, not the plate's weight: heavier plates feel more friction, but also have more inertia, and the two cancel.

When a bus brakes, the brakes slow the bus. Nothing has touched you yet, so your body carries on at 40 km/h. That is why you lurch forward: you are not thrown, the bus is slowing down under you. To slow down with it, something has to push you back with a force F = m a: your feet, your hand on the rail, or a seat.

Standing with no hand-hold, your feet can only do so much. Lean more than your feet can support and you tip: that happens once the braking passes about g × (foot length ÷ height of your middle), roughly 1.3 m/s². Normal bus braking is 1 to 2 m/s², so hold on. At 3 m/s² a 60 kg passenger needs 180 N from their grip, like holding up an 18 kg bag.

A car's seat belt and airbag exist for the same reason: in a crash the car stops in a tenth of a second and you don't, unless the belt stops you with it (see CarClear and NewtonClear). A motorcycle rider has no belt at all. Braking hard, their arms, knees and seat must hold back the whole body, around 500 N for 70 kg at 7 m/s² (MotorcycleClear).

Loads on a lorry are the same. Friction can hold a crate only while the braking is below μ g, whatever the crate weighs, because a heavier crate grips harder but also has more inertia. On a bare steel bed that is only about 3 m/s². Brake harder and the crate slides into the cab, so the rules say loads must be strapped to hold 0.8 g forwards.

Spinning has its own kind of inertia, the moment of inertia, I = Σ m r², in kg·m². It depends not just on the mass but on how far it sits from the axis: double the distance and the same mass is four times harder to spin up or stop. A spinning thing keeps its angular momentum, L = I × ω, unless something twists it.

That is the skater's trick. Arms out, she turns slowly. Pull them in and her moment of inertia drops nearly four times, so her spin speeds up nearly four times, to about 5 turns a second. Nobody pushed her: L stayed the same while I shrank. (Her energy does go up. Her arm muscles pay for it, pulling against the spin.)

A spinning bicycle wheel hung by one end of its axle doesn't fall. Gravity's twist turns the axle slowly sideways instead: precession, at a rate τ ÷ (I ω). The faster it spins, the slower and steadier it turns. It helps a moving bike a little, but the main reason a bike stays up is steering (see CycleClear and Chapter 5).

A car engine only pushes in bursts: a four-cylinder fires twice every revolution. A heavy flywheel on the crankshaft soaks up each burst and gives it back between them, so the engine turns smoothly instead of jerking (CarClear). A washing machine drum has a big moment of inertia too, which is why it takes a while to spin up and why an unbalanced load makes it shake (WasherClear).

Most scales measure weight, the pull of gravity, and then quietly divide by Earth's g to show kilograms. A spring scale stretches in proportion to the force, so on the Moon, where gravity is a sixth as strong, a 6 kg bag of rice reads about 1 kg. The rice hasn't changed.

A pan balance is cleverer. It compares the bag with known masses. Gravity pulls both sides equally, so it cancels, and the balance reads 6 kg on Earth and on the Moon. But on the International Space Station it fails too: everything there is falling round the Earth together, so nothing presses on either pan.

So how do astronauts track their mass? They use inertia instead of weight. Skylab's crews in 1973 sat in a chair on springs and let it wobble: a heavier person swings more slowly, with period T = 2π √(m ÷ k). That is an inertial balance, and it works anywhere.

On the ISS today, the SLAMMD uses Newton's second law directly. Springs pull the astronaut's arm-rest with a known, steady force, a sensor times how fast they speed up, and the computer works out m = F ÷ a to within about 0.2 kg.

Myth: things naturally slow down. Aristotle thought so, and everyday life agrees: stop pedalling and a bike rolls to a halt. But the bike isn't "running out of motion". Friction and air are pushing it back. Take them away and nothing slows it at all. A space probe coasts for decades: Voyager 1, launched in 1977, is still travelling at about 17 km/s.

Myth: heavy things are harder to keep moving on ice. On ice, keeping a sledge going takes almost no force at all, heavy or light, because friction is tiny. What's hard is starting and stopping it: that's inertia, m a. A heavy sledge slides just as far as a light one, because friction and inertia both grow with mass.

Two kinds of mass. Mass appears twice in physics: inertial mass (how hard to accelerate, F = m a) and gravitational mass (how hard gravity pulls, W = m g). Nothing says they must be equal, yet every test finds they are. That's why a hammer and a feather fall together on the Moon. Loránd Eötvös checked it with a torsion balance to a few parts in a billion around 1900; the MICROSCOPE satellite (2016–2018) got to about 1 part in 10¹⁵. Einstein took it as a principle, the equivalence principle, and built general relativity on it.

"Mass grows at high speed"? Old books say an object's "relativistic mass" rises towards light speed. Physicists today mostly don't use that idea. Mass means the rest mass, which never changes; what grows is the energy and momentum it takes to go faster, without limit, which is why nothing with mass reaches light speed.