Rolling Race Lab

Class XI · System of Particles & Rotation: a = g sinθ / (1 + k²/R²).

Pick 2–3 racers

Controls

Incline angle θ25 °

Accelerations

Solid spherea = 2.96 m/s² · t = 1.84 s

Solid cylindera = 2.76 m/s² · t = 1.90 s

Ringa = 2.07 m/s² · t = 2.20 s

Formula

Rolling without slipping:
  a = g sinθ / (1 + k²/R²)

Body              k²/R²
  Solid sphere    2/5
  Hollow sphere   2/3
  Solid cylinder  1/2
  Hollow cylinder 1
  Ring            1

Smaller k²/R² ⇒ larger a ⇒ wins.

Try this: Race a solid sphere, a solid cylinder and a ring. Order should be sphere > cylinder > ring: independent of mass and radius! The body that stores the least energy in rotation (smallest k²/R²) wins.

Rolling Race Lab

AI Summary