Theme

What stays the same

Conservation laws, and the habit of solving a problem by refusing to look at the middle of it.
−π−π/2π/2π-22angleangular velocityat rest, hanging downbalanced upside downclosed: swingingopen: going over the topdashed: the boundary Mechanics

The pendulum, and the small lie that makes it simple

A pendulum's period does not depend on how far it swings. This is one of the most useful false statements in physics, and it is worth knowing exactly how false.

00.20.40.60.8100.20.4range20°35°45°60°75°same speed, five angles45° goes furthest; 20° and 70° tie Mechanics

The angle that throws furthest, and why nobody notices

Forty-five degrees is the answer, and the maximum is so flat that a throw ten degrees off loses almost nothing. Both halves of that are worth drawing.

before23.001-1.00momentum 5.00energy 9.50after20.3314.33momentum 5.00energy 9.50energy survives too — but only because e = 1 Mechanics

Collisions are easier than forces, and momentum is the reason

Nobody knows what happens inside a collision. Momentum conservation makes that ignorance irrelevant, which is the whole trick — and energy, deliberately, is not conserved.

00.511.522.5-101positionone wavelength Waves

A wave is a shape that travels, and nothing else does

In a wave on water, no water goes anywhere. What moves is the shape — and separating the two motions is the whole of wave physics.

n = 1fundamentaln = 22× the frequencyn = 33× the frequencyn = 44× the frequency Waves

Only some notes fit, and that is where discreteness comes from

A string clamped at both ends can vibrate at some frequencies and not others. A continuous object producing a whole-number list is the oldest quantisation in physics.

+every line leaves: net flux counts the chargethe shape of the surface never enters the answer Electromagnetism

Counting what comes out, and never looking inside

Draw any closed surface. The field crossing it depends only on the charge enclosed — not on where that charge sits, not on its shape, not on anything outside.

xctlightct′x′here, nowfuturepastunreachableγ = 1.155 — the axes close on the light line together Relativity

Two axes, one speed, and a diagram that does the arguing

Put position across and time up, insist that light travels at forty-five degrees for everyone, and nearly every result in special relativity becomes something to read off rather than derive.

at restlight goes straight upmovinglight travels 1.25× as farγ = 1.250the ratio is forced by one constant speed Relativity

The clock that has to slow, and why no clock can refuse

One constant speed and one right-angled triangle force a moving clock to tick slower. The argument is Pythagoras, which is what makes it inescapable rather than merely surprising.

xctsame time, for one observersame time, for the otherABneither slicing is the right one: that is the content of relativity Relativity

Now is a choice of slicing

Two events happening at the same time is not a fact about the events. It is a fact about who is asking, and different observers slice spacetime at different angles.

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