physics

One labelled force: an arrow of a given length, from a point, at a bearing. The whole of a free-body diagram is several of these at one point, which is why it is this rather than a construct taking four forces at once — a figure with three forces should not have to leave a fourth blank.

A force with its two components drawn dashed beside it, and the right angle between them marked. along is the direction the components are taken in — 0 for the ordinary horizontal and vertical pair, the slope's angle for a block on a slope, which is the case the resolution exists for. The arithmetic is the point: the parallel component is $F\cos(\theta - \alpha)$ and the perpendicular one $F\sin(\theta - \alpha)$, and getting the sign of that difference right by hand is where the figure usually goes wrong.

A block on a slope: the ground, the incline, the block sitting on it and the angle at the foot. The block is a rectangle turned to lie on the slope, so its corners come out of the slope's own direction and normal rather than being written down — which is what a hand-drawn version of this figure never quite manages. at is how far along the slope it sits, as a fraction.

A pendulum hanging from a pivot: the string at an angle FROM THE VERTICAL, the bob, the vertical it swings about, and the angle between them.

A projectile's flight: the trajectory, the apex, and the range, from a launch speed and an angle. Everything but the curve is a consequence of those two — the range is $u^2\sin 2\theta / g$ and the apex $u^2\sin^2\theta / 2g$ — so the markers land where the curve actually goes rather than where they were dragged.

A velocity–time graph under constant acceleration, with the area under it shaded: the displacement, which is what the area IS. The line is a curve rather than a line so that integral can shade under it — the area is sampled from the curve itself, so it follows the line however the acceleration changes.

A travelling wave, with its amplitude ruled across and its wavelength braced along the axis. phase moves the wave along without changing anything else, so a step can show the same wave a quarter period later.

A thin converging lens with the three construction rays and the image they meet at. The image is where the lens equation puts it: $v = uf/(u - f)$, with the height scaled by $-v/u$ — so the rays meet AT the image rather than near it, which is the one thing a hand-drawn ray diagram cannot promise. Distances are positive: the object stands u to the left of the lens, the focal points at $\pm f$ either side. The real-image case, so u must be greater than f. Nearer than the focal point the rays diverge and the image is virtual — a different construction, with the rays extended back rather than crossing.

Refraction at a boundary: the incident ray, the normal, and the refracted ray at the angle Snell's law puts it, with both angles marked. The refracted angle is $\arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)$, worked out here rather than by the author — so the ray bends towards the normal when it should, and by as much as it should. Both angles are measured FROM THE NORMAL, as they are in the subject. The boundary runs along $y = 0$ with medium 1 above it.