Centrifugal Force of a Rotating Mass
The outward force a spinning mass throws - why rotating gear must be balanced and grinding wheels are speed-rated.
Example
You enter
- Mass weight W (lb) 2
- Radius to mass center r (in) 6
- Rotational speed (rpm) 1800
You get
- Centrifugal force 1104.3 lbf
- Acceleration 552.2 g
Details, formula, and sources
F = (W/g) omega^2 r with omega = 2 pi N/60, plus the acceleration in g and the rim speed v = omega r. A 2 lb part at a 6 in radius at 1,800 rpm throws 1,104 lbf - 552 times its own weight - at 94 ft/s (5,655 ft/min) rim speed; the force climbs with the SQUARE of speed, so 3,600 rpm quadruples it to 4,400 lbf. That is why a small imbalance is violent at speed and a chipped wheel that is safe by hand can burst at rpm. Burst stress, bearing imbalance reaction, and whirl (critical) speed are separate. A design aid; Machinery Handbook and the equipment maker govern.
omega = 2 pi N / 60; F = (W/g) omega^2 r (g = 32.174 ft/s^2, r in ft); a_g = omega^2 r / g; v = omega r.
The centrifugal (centripetal) force F = (W/g) omega^2 r and rim speed v = omega r (standard dynamics; Machinery's Handbook), by name.
The centrifugal-force relation is a standard published dynamics result; the weight, radius, and speed are the user's inputs.
Estimate. AHJ and licensed professional govern.
Field names used by the API: weight_lb, radius_in, speed_rpm, centrifugal_force_lbf, acceleration_g
- Centrifugal force F = (W/g) omega^2 r for a concentrated mass at radius rdynamics
- Speed square force grows with the square of rpm; a_g = omega^2 r/gdynamics
- Scope concentrated mass; burst stress, imbalance couple, whirl speed are separatescope of this tile