Rolling race: ring, disc, sphere and block down a ramp

Release a ring, a disc, a solid sphere and a sliding block together down a ramp. See why the acceleration is g sinθ ÷ (1 + I/mr²) and who wins.

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  1. Set ramp
  2. Release
  3. Check
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Who gets down first?

A teaching model: all four start together, the three rolling ones do not slip, the block has no friction. Slowed down to watch. g = 9.8 m/s².

Results

RacerI ÷ mr²a (m/s²)Time

Try this

  • Release them. The block wins, then the sphere, then the disc, and the ring is last.
  • The order never changes with the angle or the length. Only the times do.
  • The mass and the size of the rolling bodies do not matter: they cancel out of a.
  • A rolling body must turn as well as move, so part of its energy is spent on spinning. The more mass near the rim, the more is spent.

Check yourself

What it does

Four things start together at the top of a ramp: a ring, a disc, a solid sphere that roll without slipping, and a block that slides with no friction. They all lose the same height, but only the block puts all that energy into moving down the slope. The rolling ones must also spin, so some energy goes into rotation and they are slower.

The acceleration of a rolling body is a = g sinθ ÷ (1 + I/mr²). The ratio I/mr² is 1 for a ring, ½ for a disc and ⅖ for a sphere, and 0 for the block, so the order is always block, sphere, disc, ring. Mass and size cancel out. To see how a sliding block behaves with friction, try friction ramp, and for how a spinning body’s I affects its spin see spinning skater.

How to use it

  1. Set the ramp angle and length.
  2. Press Release and watch the four lanes (seen from above, slowed down).
  3. Read the acceleration and time for each racer in the table.

What each setting does

  • Ramp angle θ: a steeper ramp gives bigger accelerations for all.
  • Ramp length: a longer ramp means longer times (t grows as √L) but never changes the order.

Worked example

Take θ = 30° and a length of 2 m. The block has a = 9.8 × 0.5 = 4.9 m/s² and takes √(2 × 2 ÷ 4.9) = 0.904 s. The sphere has a = 4.9 ÷ 1.4 = 3.5 m/s² and takes 1.07 s. The disc has a = 4.9 ÷ 1.5 = 3.27 m/s² and takes 1.11 s. The ring has a = 4.9 ÷ 2 = 2.45 m/s² and takes 1.28 s.

FAQs

Does a heavier ring beat a lighter one? No. The mass cancels, so the same shape always takes the same time.

Why does the ring lose? Its mass is all at the rim, so for a given speed it needs the most energy to spin.

Why must friction be there for rolling? Static friction makes the body turn. It does no work when there is no slipping, so energy is conserved.

Is anything stored? No. Everything is worked out in your browser.

Where the numbers come from

  • Rolling without slipping on an incline, a = g sinθ ÷ (1 + I/mr²), with I/mr² = 1 for a ring, 1/2 for a disc and 2/5 for a solid sphere: standard Class 11 physics (system of particles and rotational motion). g = 9.8 m/s². The picture is fibub's own teaching model.

Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.

Last updated 2026-11-10.

Change log for Rolling race

  1. Add rolling-race (Class 11 Physics) Details on GitHub

Every change to fibub

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