Illustrated Physics
physics, drawn
Concept

Newtons third law — where it appears

The rule that two bodies exert equal and opposite forces on each other. For gravity it holds only if every material's active mass is the same multiple of its passive mass, and it is equivalent to the conservation of momentum.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

Thrust against the air it is supposed to be pushing on. The thrust of one F-1 engine against ambient pressure, in atmospheres. It is 6.78 meganewtons at sea level and 7.77 in vacuum — 14.6 per cent more with the air taken away. The line falls at exactly 9.787 newtons per pascal, which is the nozzle's exit area, because the term is (p_e − p_a)·A_e: the ambient pressure pushes on the exit plane from outside and there is nothing to push back on it. The account in which the exhaust shoves against the atmosphere makes the opposite prediction — thrust falling with the pressure and vanishing in vacuum — and it is not a small disagreement about a coefficient. It has the sign wrong. A rocket works better in vacuum than in air, and every engine ever fired has said so.

The push that needs nothing to push against

A rocket engine produces more thrust in vacuum than at sea level — fifteen per cent more, for the engine drawn here, and the extra is exactly the ambient pressure times the nozzle's exit area. The account in which the exhaust shoves against the atmosphere does not merely overstate a coefficient. It has the sign wrong, and every engine ever fired has said so.

mechanics · Momentum Two pulls that should be equal and opposite. Two bodies of equal passive mass, one of an ordinary material and one of a material whose active mass is 30 per cent larger than its passive mass (the difference exaggerated to be seen). Each pulls the other with its active mass and is pulled on its passive mass. The pull the unusual body exerts is therefore larger than the pull it receives, the two arrows are not equal and opposite, and the pair, with nothing outside it, accelerates towards the ordinary body. Newton's third law and the conservation of momentum both require the ratio of active to passive mass to be the same for every material, and that is a separate claim from the one torsion balances test, that passive and inertial mass agree.

The pull that has to equal the pull back

Every test of the equivalence principle drops two things and asks whether gravity pulls them equally. None of them asks whether they pull equally. A body's mass enters gravity twice — once as what is pulled and once as what does the pulling — and if the two ratios differed from one material to another, Newton's third law would fail and a lopsided body could push itself through space. The first test of this used a plastic cylinder floating in a liquid. The best uses the Moon, whose light crust is thicker on the side that never faces the Earth.

astrophysics · Equivalence principle Two pieces of current that one law makes push each other unequally. Two short elements of current a unit distance apart: element 1 pointing along the line joining them, element 2 at 45° to it. Left, the forces by the law that follows from Biot and Savart (Grassmann's): element 1 pushes nothing on element 2, because 1 points straight at it, while element 2 pushes on element 1 with a force of 0.71 units at right angles to it; the pair would feel a net 0.71 units. Right, the forces by Ampère's own law of 1826: 0.71 units each, along the line joining the elements, equal and opposite. Both laws give the same force between any two complete circuits, so no experiment on closed circuits can say which is right.

The force between pieces of a current

Ampère spent six years finding the force one short piece of current exerts on another, and the law he found is not the one used today. The modern law, which follows from the Biot–Savart field, disagrees with his for almost every pair of pieces — his obeys Newton's third law and the modern one does not. Both give exactly the same force between any two complete circuits, which is the only thing that has ever been measured. The force between two pieces of current is a quantity with two correct values, because a piece of current on its own does not exist.

electromagnetism · Ampere law

Named alongside it

The objects these essays reach for when they reach for this one.

Active gravitational massAmpere lawAmperes force lawBiot savart lawCentre of massConservationCurrent elementEfficiencyEquivalence principleField momentumGravitational massImpulse

All concepts