Every essay
Mechanics
Motion, force, and the quantities that refuse to change.
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.
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.
The slope, and the two directions that make it easy
An inclined plane looks like a harder problem than a flat one. Split the weight into two components chosen to suit the slope and it becomes an easier one.
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.
The hill that gives it back, and the forces that do not
Potential energy turns a question about motion into a picture of a landscape. It works for gravity and springs, it fails for friction, and the difference between those two cases is the whole of what makes energy useful.
Turning is an acceleration, and constant speed does not help
An object going round a circle at unchanging speed is accelerating hard, all the time, toward a point it never reaches. The construction that shows this needs two arrows and no calculus.
The period that depends on the swing, computed exactly
A pendulum's period is not independent of amplitude. The exact answer is an elliptic integral, it has no elementary form, and plotting it shows precisely where the famous approximation earns its keep and where it collapses.
Waves
Oscillation, and everything that turns out to be an oscillation.
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.
When two waves meet, they simply add
Waves pass through each other unchanged and their displacements add point by point. From that one impoverished-sounding rule comes interference, beats, and the evidence that light is a wave at all.
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.
The note that changes on approach, and the two ways of getting it
A moving source and a moving listener produce different formulas for the same shift, because the medium is watching. The difference is small, real, and the reason light had to be treated differently.
The frequency that gets an answer, and the quarter cycle nobody mentions
Push an oscillator at its own frequency and the response grows enormously. The reason is not that the push is in step with the motion — at resonance it is a quarter cycle out, and that is precisely why it works.
Optics
Light, and the small number of rules it obeys.
The bend at the boundary, and what it is really about
Light changes direction when it changes speed. Snell's law is the geometry of that statement, and it can be derived without knowing anything about light at all.
What a lens is doing, and why three rays are enough
A lens bends every ray that reaches it. The construction uses three, because three are all that can be drawn without calculation — and any three that meet prove all the rest do.
The angle past which light cannot leave
Snell's law asks for the sine of an angle greater than one, and no such angle exists. What happens instead is a perfect mirror made out of nothing but a change of speed.
Electromagnetism
Charge, field, and the lines drawn between them.
Field lines are a choice, not a discovery
Nothing in space is arranged in lines. The lines are a drawing convention — and an unusually good one, because three separate facts about the field survive the translation.
The field before the lines were drawn on it
A field is a vector attached to every point of space. Drawing it as arrows on a grid is honest and ugly; drawing it as lines is beautiful and throws information away.
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.
Thermodynamics
Heat, disorder, and the one law with a direction in it.
The speeds in a still room
The air in a quiet room is not still. Every molecule in it is moving at hundreds of metres per second, and temperature is a single number summarising an entire distribution.
Entropy is a count, and the arrow of time is arithmetic
Nothing in mechanics prefers a direction. Entropy is not a force pushing things toward disorder — it is the observation that some outcomes have vastly more ways of happening than others.
The ceiling on every engine, set before it was designed
There is a maximum efficiency no heat engine can exceed, and it depends on nothing but two temperatures. Not the fuel, not the working substance, not the cleverness of the engineer.
Relativity
Space and time, drawn on the same axes.
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.
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.
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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