Centripetal Acceleration (a = ω²r)
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Because v = ωr, the familiar a = v²/r can be rewritten as ω²r — often more convenient, since machines are usually specified by rotation rate. Note the reversal: at fixed speed v, a larger radius means gentler acceleration, but at fixed spin rate ω, a larger radius means harsher acceleration. A laboratory centrifuge at 10,000 rpm (ω ≈ 1047 rad/s) with a 10 cm rotor pulls ω²r ≈ 110,000 m/s² — over 11,000 g.
Centripetal Acceleration (a = ω²r)
Where
- = Centripetal acceleration
- = Angular velocity
- = Radius
Missing one of these? Work it out first, then come back
- Centripetal acceleration — Centripetal Acceleration (a = v²/r), Newton's Second Law
- Angular velocity — Angular Velocity (ω = θ/t), Angular Velocity from Period
- Radius — Centripetal Acceleration (a = v²/r), Centripetal Force (F = mv²/r)