21:15, a slate table, late
Five Eighths stands because it has nowhere lower to go. A top has, and stands anyway, but only while it spins: upright is stable for it above a certain speed (a² > 4 in the formula), and below that the smallest nudge grows. Leaning, a spinning top does not fall: gravity turns its axis sideways instead of down, and the axis goes slowly round the vertical, at a rate that goes as one over the spin, so the slower it spins, the faster it circles. Let go leaning and at rest, the axis also nods as it goes. Lagrange wrote the equations in 1788, and the figure is their solution, seen from above, for a top with nothing rubbing at its point, spinning 1.8 times as fast as it needs to sleep and let go at 12°: ten nods to one turn. Friction at the point soon rubs the nods out, and what is left is the red circle; watch it hurry as it tires.
Objects · Solid brass spinning top
The Top
CHF 90 working price
For the end of a long proof: draw a circle, spin it inside, and see what standing up costs.
A small top turned from one piece of brass, with a stick of chalk to draw its circle. Spun hard it stands upright and looks asleep. It is not at rest: it stands only while it spins.
A study: nothing can be ordered yet. The photograph is a generated image, not a picture of a made piece or of a real person.
- Solid brass, turned in one piece and left raw: 38 mm across, 38 mm tall, about 100 g; it darkens with handling and stays bright where the fingers spin it
- A stem 5 mm thick to spin between finger and thumb. The point is the one part that is not brass: hardened steel, 1 mm in radius, pressed in
- One stick of white chalk in the box, to draw its circle on slate: the game is to stay inside it. An arrow on the circle marks the way you spun it, which is also the way its lean will go round
- By calculation it sleeps above about twelve turns a second; finger and thumb give it twenty or thirty. Leaning, it goes round the vertical about once a second, and faster as it slows
- Numbered on the end of the stem; a slate box lined in felt. Nothing on it is red
