i About this experiment — click to learn the physics ▼
What you're looking at
A round object rolls down a ramp without slipping — the contact point doesn't skid, so the object both slides forward and spins, locked together. The painted spoke lets you see the spin. The surprising result: how fast it rolls down depends only on its shape, not its mass or size.
The no-slip condition
Rolling without slipping ties the forward speed to the spin rate through the radius:
Every metre the object advances, the rim turns by exactly that arc length — so a faster spin means a faster roll.
Why shape decides the race
Gravity has to do two jobs at once: speed the object up and spin it up. How much goes into spinning depends on the moment of inertia I — how far the mass sits from the axis. Solving Newton's laws for the ramp gives:
The mass and radius cancel, leaving only the dimensionless ratio I/mr². Mass concentrated near the centre (a solid sphere) is easy to spin, so more energy goes into motion and it accelerates fastest. Mass out at the rim (a hoop) is hard to spin, so it lags behind.
| Shape | I / mr² | Rotational energy |
|---|---|---|
| Solid sphere | 0.40 | 29% — fastest |
| Solid disc / cylinder | 0.50 | 33% |
| Hollow sphere | 0.67 | 40% |
| Ring / hoop | 1.00 | 50% — slowest |
Energy split
At the bottom the lost height has become kinetic energy, shared between motion and spin. The fraction tied up in spinning is fixed by the shape: rotational fraction = (I/mr²) / (1 + I/mr²). A hoop puts half its energy into spinning, a solid sphere less than a third — which is exactly why the sphere ends up moving faster.
Things to try
Change the mass and radius and confirm the acceleration never budges. Then hit Race all 4 shapes and watch them finish in the order sphere → disc → hollow sphere → hoop, every time.