Centripetal Force on a Roller Coaster Loop

The Physics

Centripetal force keeps the coaster on a circular path through a loop. It’s supplied by the track pushing inward toward the circle’s center.

Formula

Fc = (m × v²) / r

• Fc = centripetal force
• m = coaster mass
• v = velocity
• r = loop radius

Why It Matters

Insufficient centripetal force would cause the train to leave the track. Engineers design loop geometry and speed profiles to maintain safe, comfortable forces throughout the inversion.