• Pixel-art sticker of Loopet, personifying Loop-the-Loop, with the caption “Fast At The Top Or I Fall.”

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Loopet

Loop-the-Loop Physics

\[v_{\text{top}} \geq \sqrt{g R}\]
$4.99 USD
$4.99 USD
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Meet Loopet, a coaster cart who must be quick at the top of the loop or drop off. Gravity alone must turn him there, so the minimum speed is √(gR): about 9.9 m/s for a 10 m loop. Without friction, he must start at least 25 m up. 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 Loopet, a coaster cart who must be quick at the top of the loop or drop off the track.

At the very top of a vertical loop, the cart is upside down. Gravity and the push of the track both point down, toward the centre of the loop. Together they must supply the inward force that keeps the cart moving in a circle.

The slowest safe speed is when the track push drops to zero and gravity alone does the job. Then v = √(gR). For a loop of radius 10 m that is √(9.81 × 10) ≈ 9.9 m/s, about 36 km/h.

Starting from rest with no friction, the cart has to begin at least 2.5R above the bottom, which is 25 m for this loop. Real rides start higher to allow for friction.

Modern coaster loops are not perfect circles. They are taller and narrower, so riders feel less extreme forces at the bottom.

Equations

\[v_{\text{top}} \geq \sqrt{g R}\]
SymbolMeaningUnit
\(v_{\text{top}}\) speed at the top of the loop \(\mathrm{m/s}\)
\(g\) gravitational acceleration \(\mathrm{m/s²}\)
\(R\) radius of the loop \(\mathrm{m}\)

Sources

  1. OpenStax University Physics Vol. 1 — Centripetal Force
  2. OpenStax University Physics Vol. 1 — Conservation of Energy
  3. Wikipedia — Vertical loop

Field notes

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