For a rigid body rotating about a fixed axis at N rpm, angular speed is ω = 2πN/60. A point at radius r has tangential speed v = ωr. All points share angular speed, while linear speed increases in direct proportion to radius.
Rigid-Disc Rotary Kinematics
Calculate ideal angular speed, selected-point tangential speed, rim speed and revolution period for a rigid disc.
Equation Used
- The body is rigid and rotates about a fixed axis.
- All points share the selected constant angular speed.
- Point percentage is clamped to the selected rim radius.
- Slip, runout, deformation, acceleration, loads, stresses and ratings are excluded.
The displayed disc is normalized; selected diameter affects calculated radii and speeds, not the on-screen scale.
Rigid-body rotary motion
A fixed-axis rigid body advances through the same angle at every radius. The selected disc diameter sets the rim radius, and point radius is selected as a percentage of that rim value.
The animation shows the radius vector and its perpendicular tangential-velocity direction. It assumes ideal rigid rotation without slip, deformation, runout or changing speed.
What the calculator determines
Select rotational speed, diameter and point-radius percentage. The calculator returns angular speed, tangential speed at the selected point, rim speed and revolution period.
It does not size a shaft, bearing, motor, wheel or transmission and does not calculate torque, power, stress, critical speed, balance, fatigue, bearing life or a safe operating speed.
Ideal rotary kinematics
ω = 2πN/60 converts revolutions per minute to radians per second. With D in millimetres and point percentage q, r = (D/2000)(q/100) metres, then v = ωr. Rim speed uses r = D/2000. For N > 0, period is 60/N seconds or 60,000/N milliseconds.
Selected-input example
At 3,000 rpm with a 600 mm diameter and the point at 100% rim radius, ω = 314.159 rad/s, rim and point speed are 94.248 m/s, and period is 20.000 ms/rev.
These are exact ideal conversions for the selected values, not evidence that any particular disc or machine can safely operate there.
Scope and correction boundary
The calculator's kinematic identities are retained. The former article added unsupported product specifications, shaft and bearing rules, tolerances, critical-speed advice, failure diagnoses and a fabricated loom example that cannot be inferred from speed and diameter alone.
Those claims and the unrelated video are removed. Apply manufacturer ratings and a qualified rotor-dynamics or structural analysis before selecting real rotating equipment.
Questions
Do all points have the same linear speed?
No. They share angular speed. Tangential speed is zero on the axis and rises linearly with radius.
What happens at zero rpm?
Angular and tangential speeds are zero. The calculator reports period as zero rather than an infinite numeric value.
Is calculated rim speed a safe speed?
No. Safe speed depends on the actual component, material, geometry, stress, balance, mounting, condition and manufacturer limits.
Does diameter determine torque or power?
No. Torque and power require load or force information in addition to kinematics.
Technical references
- OpenStax Physics, Angle of Rotation and Angular Velocity — defines angular velocity and the fixed-axis relation between angular and tangential motion.
- NIST Special Publication 811 — SI units and conversion guidance for coherent quantities.
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