A solid sphere released on an incline only rolls without slipping if static friction is strong enough. Balancing Newton's second law with the torque equation for a solid sphere (I = ⅖mr²) gives a downhill acceleration of a = (5/7)·g·sinθ — independent of mass or radius — but only while μ ≥ (2/7)·tanθ.
When the ramp is steeper than that (a low-friction, steep-angle combination), the ball can't grip: it slips. Kinetic friction then sets both accelerations independently — translation speeds up faster than rotation can keep up (a = g·sinθ − μg·cosθ, while spin-up is driven separately by the friction torque) — so the ball reaches the bottom moving faster but spinning slower than a pure roll would predict.
On the flat section, gravity no longer drives the ball forward; only rolling resistance (a small drag from surface/ball deformation, scaled here from the friction slider) slows it down until it comes to rest, unless it reaches the wall first — where it bounces back using that material's real coefficient of restitution (rubber ≈0.68, marble ≈0.34, steel ≈0.16, brass ≈0.20), the same values a physical experiment would show.
- Material sets density (hence mass) and the wall's coefficient of restitution.
- Radius changes mass (∝r³) and how far the mass sits from the spin axis.
- Ramp angle and friction together decide whether the ball rolls cleanly or slips.
- Gravity (with Moon/Earth/Mars presets) scales every acceleration in the simulation.