Circular-motion arithmetic, not a safe-speed selector

Controlled Rotor Peripheral Kinematics Calculator

Convert a documented radius or diameter and rotational speed into angular speed, peripheral speed and centripetal-acceleration magnitude. The calculation does not select an operating speed, balance grade, guard, tool retention or power.

Exact unit conversionsNo “optimal” speed bandsNo G-grade selectionNo retention-force claim

Documented point on a rotating body

Do not use this result as a maximum or safe operating speed. Tip speed and radial acceleration alone cannot verify rotor stress, tool or pin loads, impact, fatigue, critical speed, overspeed margin, guarding, containment, balance tolerance, bearing load, cutting performance or power. Use the machine manufacturer’s controlled limits and a qualified engineering risk assessment.

Geometry inputState whether the measured length is a diameter or a radius to the evaluated point
Documented lengthPositive plain decimal; not a nominal housing or rotor-body size
Documented rotational speedPositive plain decimal at the same operating state
Geometry, speed and source recordIdentify the point, drawing/measurement, speed source, machine and operating state
I confirm that the radius/diameter reaches the evaluated point and that geometry and speed describe the same documented machine state.
I understand that this is kinematics only and does not establish a safe speed, tool force, balance grade, power requirement, guard or containment design.

Kinematic result

Peripheral speed magnitude v

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Evaluated radius r

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Velocidade angular ω

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Other speed units

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Centripetal-acceleration magnitude aᵣ

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Standard-gravity multiple

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Frequência rotacional

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Rotation period

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General circular-motion relations

r = D / 2 (when diameter is entered)
ω = 2πn / 60 for n in r/min
v = ωr
aᵣ = v²/r = ω²r
g-multiple = aᵣ / gₙ ; gₙ = 9.80665 m/s²

These are general kinematic relations, not formulas mandated by an ISO balance standard. The acceleration shown is the inward centripetal-acceleration magnitude of the evaluated point in an inertial description. “Centrifugal force” in a rotating-frame description and actual attachment loads require a defined mass model and complete load path; this page deliberately does not calculate them.

NIST lists one revolution as 2π radians and recognizes r/min for rotational frequency in machinery specifications. Inch and foot conversions use exact SI definitions; the standard-gravity multiple uses the NIST value gₙ = 9.80665 m/s².

What this result cannot establish

There is no universal “optimal” tip-speed range for mulchers, chippers, shredders or hammer mills. Product geometry, tools, material, feed, impact, screen, drive, structure and OEM validation control the duty.
Power is not universally proportional to the cube of rotor tip speed for these machines. That affinity-law scaling belongs to specific dynamically similar fluid-machine conditions and was removed.
ISO 1940-1:2003 is withdrawn. ISO 21940-11:2016 with Amendment 1:2022 is the current ISO record for procedures and residual-unbalance tolerances of rotors with rigid behaviour; it does not turn tip speed into an automatic G6.3 recommendation. Flexible rotors are outside that part.
As a United States example, OSHA 29 CFR 1910.212(a)(1) requires guarding against hazards including rotating parts and flying chips. Applicable jurisdiction, machine-specific requirements and OEM instructions must be checked separately; a velocity result is not a guard or containment design.

Official evidence

NASA Glenn — Angular Displacement, Velocity and Acceleration

Official explanation of angular velocity and the tangential relation v = ωr.

NASA GSFC — circular-motion acceleration derivation

Official explanation of centripetal acceleration magnitude a = v²/r.

NIST SP 811 Appendix B.9

Official revolution-to-radian and standard-gravity conversion values.

NIST SP 811 Chapter 8

Official SI style guidance recognizing r/s and r/min for rotational frequency.

ISO 21940-11:2016 + Amd 1:2022

Official current-status and scope record for rigid-rotor balancing procedures and tolerances.

ISO 1940-1:2003 lifecycle record

Official record showing withdrawal and revision by ISO 21940-11:2016.

OSHA 29 CFR 1910.212

Current United States general machine-guarding requirement; cited as a jurisdiction-specific safety example, not a universal design formula.