• Pixel-art sticker of Rollix, personifying Rolling Resistance, with the caption “Even Rolling Costs A Little.”

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Rollix

Rolling Resistance Physics

\[F_{\text{rr}} = C_{\text{rr}} N\]
$4.99 USD
$4.99 USD
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Meet Rollix, a rubber tyre who rolls happily but always loses a little energy as heat. Rolling resistance is a small coefficient times the normal force, about 0.01 for car tyres. A 1500 kg car feels about 150 N, costing about 3.7 kW at 25 m/s. 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 Rollix, a rubber tyre who rolls along happily but always loses a little energy on the way.

A perfect wheel on a perfect road would roll forever. Real tyres squash a little where they touch the ground and spring back as they roll on. Rubber does not spring back perfectly, so some energy is lost as heat in every turn. The road surface deforms a little too.

The result is a small backward force called rolling resistance, F_rr = C_rr N. The coefficient C_rr is tiny compared with sliding friction. A good car tyre on asphalt has C_rr ≈ 0.01. A steel train wheel on a steel rail has C_rr ≈ 0.001.

A 1500 kg car presses on the road with a normal force of about 14 700 N, so its rolling resistance is about 150 N. At 25 m/s that costs about 3.7 kW.

Higher tyre pressure squashes the tyre less and lowers C_rr, which is why cyclists pump their tyres hard and why soft sand is so tiring to ride through.

Equations

\[F_{\text{rr}} = C_{\text{rr}} N\]
SymbolMeaningUnit
\(F_{\text{rr}}\) rolling resistance force \(\mathrm{N}\)
\(C_{\text{rr}}\) rolling resistance coefficient \(\mathrm{dimensionless}\)
\(N\) normal force \(\mathrm{N}\)

Sources

  1. Wikipedia — Rolling resistance
  2. OpenStax University Physics Vol. 1 — Rolling Motion

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