TORQUE

why the same dumbbell grows heavier as the arm rises, and how to work it out in advance

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

Formats: A4 · A3 · A2
What you get: Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject: science · everyone · memo · gym

Torque is force times lever arm; for a hanging weight the lever arm is the horizontal distance from the axis of rotation. The shares in the chart are the sine of the angle; g = 9.80665 m/s² is the standard value adopted by the 3rd CGPM (1901).

HALF ARRIVES AT THIRTY DEGREES

sin 30° is exactly one half: a third of the way up, the dumbbell already turns the shoulder with 50% of the maximum torque. The last 15 degrees of the lift add only 3 percentage points — the top of the arc is nearly flat.

The law also works in reverse: double the lever arm and the same force turns twice as hard — which is why a long wrench shifts what a short one cannot.

On the sheet

Torque is force times lever arm; for a hanging weight the lever arm is the horizontal distance from the axis of rotation. The shares in the chart are the sine of the angle; g = 9.80665 m/s² is the standard value adopted by the 3rd CGPM (1901).
Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
Nothing about how it was made: the sheet carries only what the reader needs.

Printing

Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
White background and sparing fills — it prints on a home printer without draining the cartridge.
Margins of at least 10 mm: a home printer cannot print to the edge.
No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 7 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

TORQUE

HALF ARRIVES AT THIRTY DEGREES

On the sheet

Printing

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