• Pixel-art sticker of Twirlix, personifying Rotational Kinetic Energy, with the caption “Twice The Spin, Four Times Energy.”

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Twirlix

Rotational Kinetic Energy Physics

\[K = \frac{1}{2} I \omega^2\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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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 Twirlix, a heavy flywheel who stores energy by spinning.

A spinning object has kinetic energy even when it is not going anywhere, because every bit of it moves in a circle. For rotation, mass is replaced by the moment of inertia I, which measures how much mass there is and how far it sits from the axis. Speed is replaced by the angular speed ω in radians per second, so the energy is K = ½Iω².

Take a solid disc flywheel of mass 20 kg and radius 0.3 m. Its moment of inertia is I = ½mR² = 0.5 × 20 × 0.09 = 0.9 kg·m². Spinning at 100 rad/s, about 955 revolutions per minute, it stores K = 0.5 × 0.9 × 100² = 4500 J. Double the spin to 200 rad/s and it stores 18,000 J, four times as much.

Engineers use flywheels to smooth out the jerky output of engines and to store energy for short bursts. Some energy storage systems spin their flywheels inside a vacuum to cut air drag.

Spin cannot rise forever. The stress in the rim grows with ω², so every flywheel has a safe top speed, and friction in its bearings slowly drains the stored energy.

Equations

\[K = \frac{1}{2} I \omega^2\]
Symbols
SymbolMeaningUnit
\(K\) rotational kinetic energy \(\mathrm{J}\)
\(I\) moment of inertia about the axis \(\mathrm{kg·m²}\)
\(\omega\) angular speed \(\mathrm{rad/s}\)