• Pixel-art sticker of Wheela, personifying Rolling, with the caption “No Skid, Just Roll.”

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Wheela

Rolling Physics

\[v = \omega r\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Meet Wheela, a wheel who rolls without ever skidding: each turn carries her centre forward one circumference, so v = ωr. Her contact point is momentarily at rest, while her top moves at twice the centre's speed. 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 Wheela, a wheel who rolls smoothly without ever skidding.

A wheel rolling without slipping does two things at once: it spins, and its centre moves forward. Because the contact point does not slide, each turn carries the centre forward exactly one circumference, 2πr. That gives a simple link between speed and spin: v = ωr. Surprisingly, the point touching the ground is momentarily at rest, while the top of the wheel moves forward at twice the centre's speed.

A bicycle wheel of radius 0.35 m moving at 5 m/s spins at ω = v/r = 5 / 0.35 ≈ 14.3 rad/s, a little over two turns per second.

Speedometers and bike computers use this link, counting wheel turns and multiplying by circumference. Static friction at the contact point is what lets wheels roll, which is why braking without skidding stops a car more effectively than locking the wheels.

Real tyres flex, so the effective radius is a bit smaller than the outer radius. On ice or in hard braking the wheel can slip, and then v = ωr no longer holds.

Equations

\[v = \omega r\]
Symbols
SymbolMeaningUnit
\(v\) speed of the wheel's centre \(\mathrm{m/s}\)
\(\omega\) angular speed of the wheel \(\mathrm{rad/s}\)
\(r\) radius of the wheel \(\mathrm{m}\)