The Physics of Roller Coasters
A roller coaster is a masterclass in energy and circular motion. No engine pushes the cars after the first lift hill — gravity and the track do everything, trading height for speed and back again.
Energy conservation sets the speed
Ignoring friction, mgh at the top becomes ½mv² at the bottom. A 50 m first hill gives v = √(2gh) ≈ 31 m/s (~112 km/h) — which is why the first hill is always the tallest: it banks the energy for the whole ride.
G-forces are just the normal force
That pressed-into-your-seat feeling is the track pushing on you. At the bottom of a dip, N = mg + mv²/r; over a crest, N = mg − mv²/r — go fast enough over a sharp crest and N hits zero: weightlessness.
Clothoid loops, not circles
Modern loops are teardrop-shaped (clothoids), tighter at the top. This keeps the required centripetal force — and the g-force on riders — roughly constant instead of spiking painfully at the bottom of a circular loop.
Friction and braking
Rolling resistance and air drag constantly steal energy as heat, so each hill is lower than the last. Magnetic eddy-current brakes at the end convert the remaining kinetic energy silently, with no touching parts.
Try this yourself
- Estimate a coaster's top speed from its tallest hill using v = √(2gh) and compare with the park's claimed number.
- Notice where you feel heaviest and lightest on a ride — map each feeling to the normal force.