✓ Sources checked · 10 September 2026 · View verification
In a roller-coaster loop, gravity and contact forces together provide the required inward acceleration. The seat force a rider feels is not always equal to mv²/r by itself.
By Matan · Updated
At the bottom of a circular segment
Taking upward toward the centre, N − mg = mv²/r. Therefore N = m(g + v²/r). The rider can feel more strongly supported than at rest because the seat must both oppose weight and provide upward acceleration. [1]
Worked rider reading
For an illustrative 60 kg rider, speed 10 m/s, curvature radius 20 m and g = 9.8 m/s², the required inward acceleration is 5.0 m/s². At the bottom, N = 60(9.8 + 5.0) = 888 N, compared with weight 588 N.
At the top
In a simplified top-of-loop arrangement with inward contact force, N + mg = mv²/r. Gravity now helps provide inward acceleration. If a calculation predicts an impossible contact direction for the assumed arrangement, the contact model must change. Real restraints and wheel assemblies can exert forces beyond a simple freely supported point-mass model.
What happens without a constraint?
Initial release velocity is tangent to the path, but subsequent motion is not a straight line if gravity still acts. A released object becomes a projectile under the appropriate forces.
Real track shape
Use the local curvature radius, not one radius for every part of a noncircular loop. This example explains a force balance and does not certify a ride design.
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How this article was checked
Sources checked; calculations checked where shown. The definitions, model assumptions and main explanatory claims were cross-checked against the sources below. Worked-example arithmetic and units were checked separately. These examples are illustrative calculations, not experimental measurements.
Source cross-check and editing assisted by AI. No independent human scientific review is recorded for this revision. The check applies to the version dated 10 September 2026; it is not a guarantee that every possible interpretation is correct.
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Sources and further reading
- OpenStax: Vertical circular motion — Vertical circular motion.
- OpenStax: Motion after release — Motion after release.
Cite this article
Matan. “Centripetal Force and Other Roller Coaster Adventures.” Your Physicist. Originally published 2026-06-11; updated 2026-09-10. https://your-physicist.com/centripetal-force-and-other-roller-coaster-adventures/
Revision history
: Added a checked rider support force and corrected the unconditional straight-line release claim. Added linked sources and a transparent verification record.
