How do you calculate relative centrifugal force (RCF) from RPM and rotor radius?

• A. RCF = 1.118 x 10^-5 x r x (RPM)^2, Where r Is The Rotor Radius In Cm.
• B. RCF = (RPM)^2 / r.
• C. RCF = 0.5 x RPM x r.
• D. RCF = RPM / r.

Answer: (A)

The idea is that relative centrifugal force comes from how fast the rotor is spinning and how far out the sample sits. The centrifugal acceleration at the radius is a = ω^2 r, where ω is the angular speed. Since ω = 2πN/60 (N in RPM), and RCF is a/g with g ≈ 980 cm/s^2, the algebra gives a constant that converts RPM and radius (in cm) directly to RCF: RCF = 1.118 × 10^-5 × r (cm) × (RPM)^2.

For example, with a rotor radius of 5 cm and 10,000 RPM, RCF ≈ 1.118e-5 × 5 × (10,000)^2 ≈ 5,590 g. If you’re using millimeters for the radius, use RCF ≈ 1.118 × 10^-6 × r (mm) × (RPM)^2.

This is why the correct formula multiplies the square of RPM by the radius and a constant; the other options don’t follow from a = ω^2 r and the g conversion.