• Pixel-art sticker of Conix, personifying Conical Pendulum, with the caption “I Swing In A Circle.”

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Conix

Conical Pendulum Physics

\[T = 2\pi\sqrt{\frac{L\cos\theta}{g}}\]
$4.99 USD
$4.99 USD
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Meet Conix, a brass weight who swings round in a flat circle instead of back and forth. Gravity and string tension turn him, with period 2π√(L cosθ/g): about 1.87 s for a 1.0 m string at 30°. His mass never matters. Steam-engine governors used spinning balls like him. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Conix, a brass weight who swings round in a flat circle instead of back and forth.

If you set a pendulum bob moving sideways, it can travel in a horizontal circle while its string sweeps out a cone. Gravity pulls down, the string pulls along its length, and together they give the inward force needed to keep the bob turning.

The time for one lap is T = 2π√(L cosθ/g), where θ is the angle between the string and the vertical. For a string 1.0 m long at 30°, T ≈ 1.87 s. Swing wider and cosθ gets smaller, so each lap gets quicker.

Strangely, the mass does not appear at all. A heavy bob and a light bob on the same string at the same angle keep exactly the same time.

Old steam engines used spinning balls like Conix as governors. When the engine sped up, the balls flew outward and a linkage closed the steam valve.

Equations

\[T = 2\pi\sqrt{\frac{L\cos\theta}{g}}\]
SymbolMeaningUnit
\(T\) time for one lap \(\mathrm{s}\)
\(L\) length of the string \(\mathrm{m}\)
\(\theta\) angle of the string from vertical \(\mathrm{rad}\)
\(g\) gravitational acceleration \(\mathrm{m/s²}\)

Sources

  1. OpenStax University Physics Vol. 1 — Centripetal Force
  2. Wikipedia — Conical pendulum
  3. NIST CODATA — standard acceleration of gravity

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