Science Puzzle
Which Rolls Down the Ramp First?
A solid ball, a solid cylinder and a hoop are lined up at the top of three identical ramps. They're all different. The cylinder is the heaviest and much the widest; the ball is the smallest and lightest; the hoop is a thin ring with nothing in the middle. All three are released at the same moment and roll without slipping.
Which one reaches the bottom first?
The Answer
The ball wins, the cylinder comes second and the hoop comes last. It would happen in that order every time, whatever their sizes and masses.
A sliding block would turn all of its lost height into speed. A rolling object can't, because it has to share its energy between two jobs: moving down the slope and spinning. The more energy goes into spinning, the less is left for speed.
How much goes into spin depends on where the object keeps its mass. Mass far from the centre is hard to set spinning, because it has to travel round a big circle. A hoop has all of its mass out at the rim, so half its energy goes into spinning. A solid cylinder has its mass spread from rim to centre, so a third goes into spin. A solid ball keeps more of its mass close to the middle, and only two sevenths goes into spin. That leaves the ball the most energy for speed. From a drop of 1 metre, the ball reaches the bottom at about 3.7 metres per second, the cylinder at about 3.6 and the hoop at only about 3.1.
Mass and size cancel out. A heavier object gains more energy rolling downhill, but needs exactly that much more to get it moving, just as in free fall. A wider object spins more slowly for the same speed, in exactly the right proportion. Only the shape matters, which is why a marble beats a solid wooden rod, and the rod beats a bangle.
The principle: Rotational inertia. A rolling object shares its energy between moving and spinning, and the further its mass lies from the axis, the more energy goes into spin, so it rolls more slowly regardless of its mass or size.