Home▸Physics & Mechanics▸Rolling Motion Race Simulator

⚙️ Rolling Motion: Why the Sphere Always Wins

Interactive 3D incline with a sphere, cylinder and hoop racing down it, where adjusting each shape's moment of inertia shows how mass distribution determines rolling acceleration.

Physics & Mechanics3DModerate60 FPS

A sphere, cylinder and hoop of identical mass and radius race down a 3D incline, plus a fully adjustable "mystery" shape and an optional frictionless sliding block, showing how moment of inertia — not mass — decides who wins.

🔬 What It Demonstrates

For rolling without slipping, acceleration down a slope is a = g·sinθ / (1 + k²), where k² encodes how far mass sits from the rotation axis. Mass and radius cancel out entirely — only the shape's mass distribution matters.

🎮 How to Use

Adjust the incline angle and watch every racer's acceleration scale together. Drag the mystery shape's k² slider between sphere-like and hoop-like values and watch it slide up or down the finishing order. Toggle a frictionless block for a non-rotating baseline.

💡 Did You Know?

Because a depends only on k² and θ, a bowling ball and a marble reach the bottom of a ramp at the same time — but a hollow pipe of the same size always loses to a solid rod.

⚙ Under the hood

Interactive 3D incline where racing a sphere, cylinder and hoop down together shows how differing moments of inertia determine which shape always wins.

rolling-motionmoment-of-inertiarotational-dynamicsenergy-conservationclassical-mechanicsphysics

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install