Rolling and sliding
Why a ball beats a crate down a slope, and a hoop loses to both.
Something rolling down a slope has to do two things with the energy it gains: move, and spin. How much goes into spinning depends on how the mass is arranged. A solid ball keeps most of its mass near the middle and spends little on spin; a hoop has all of its mass at the rim and spends a great deal.
That is why a solid ball beats a solid cylinder, which beats a hoop, whatever they weigh and whatever they are made of. A crate that slides rather than rolls spends nothing on spinning at all and would win, if friction were not taking its share.
| Quantity | Symbol | How it is worked out | Unit |
|---|---|---|---|
| Moment of inertia | I | how the mass is spread about the axis | kilogram metres² |
| Rolling energy | E | ½mv² + ½Iω² | joules |
Race them in the app: a ball and a block on the same slope, a meter reading speed on each. The graph of the two speeds is the answer.
Open the ramp scene in the app to watch this one run.