Circular Motion — Enriched Simulation

Speed, tension, KE and ω are all constant. Tension supplies the centripetal force entirely.

T = mv²/r | ω = v/r | KE = ½mv²

Speed and tension vary with height. Energy conservation links position to speed.

v² = v₀² − 2gr(sinθ − 1) | T = mv²/r + mg·sinθ

KE = ½mv² | PE = mgr(1 − cosθ) | KE + PE = constant

Minimum speed at top to keep the string taut: v_top ≥ √(gr)
Minimum speed at bottom to complete the circle: v₀ ≥ √(5gr)
String breaks when T > T_break (typically at the bottom)
After break/slack: the stone follows a parabolic projectile path (shown in green dots)

Circular Motion — Live Simulation