Practice

Fc = mv²/r Formula – Centripetal Force Practice

Fc = mv²/r — Centripetal force for uniform circular motion

For an object of mass m at speed v in a circle of radius r, the required centripetal force is Fc = mv²/r toward the center. Also a = v²/r and F = ma.

Guide — how to use this formula

1. 1. Convert speed to m/s and use radius in metres.
2. 2. Fc = mv²/r; rearrange for v, r, or m.
3. 3. On a flat turn, friction often supplies Fc: μ ≥ v²/(rg).
4. 4. With period T: v = 2πr/T first.

Derivation

Centripetal acceleration has magnitude v²/r; Newton’s second law then gives the force:

1. Acceleration:
   a_c = \frac{v^{2}}{r}
2. Force:
   F_c = ma_c = \frac{mv^{2}}{r}

Use path radius, not diameter. Convert km/h → m/s before squaring v.

Examples

Example: 2 kg, 4 m/s, r = 2 m

Fc = 16 N.

Example: find v

Fc = 32 N, m = 2 kg, r = 2 m → v = √32 ≈ 5.7 m/s.

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