Convert Radians per second to Hertz (rotational)

The Radian per second (symbol: rad/s) is a unit of angular velocity. The SI unit of angular velocity (ISO 80000-3 §3-7), equal to the rate of change of angular displacement in radians per second. rad/s is the native unit of every physics and engineering formula involving rotational motion: rotational power P = τ·ω (torque × angular velocity), angular momentum L = I·ω (moment of inertia × ω), rotational kinetic energy KE = ½·I·ω², centripetal acceleration a = ω²·r, and the time-derivative form of angular position θ(t) where ω = dθ/dt. Mechanical engineering (drivetrain dynamics, turbomachinery analysis per ASME PTC 6), robotics control loops (PID position-loop tuning in radians per second for joint actuators), gyroscope output (MEMS rate gyros report rad/s natively on the I²C/SPI register), and physics simulations (Bullet Physics, Newton Dynamics, PhysX) all work in rad/s. Reference values: Earth's rotation 7.27 × 10⁻⁵ rad/s (one full turn per 24 h ≈ 86,164 s sidereal day); a typical automotive crankshaft at 6,000 RPM = 628 rad/s; helicopter rotor 30-40 rad/s. 1 rad/s ≈ 9.5493 RPM.

Radians per second are commonly used in motor specifications, rotating machinery, and mechanical design.

The Hertz (rotational) (symbol: Hz) is a unit of angular velocity. Rotational frequency expressed in cycles per second — dimensionally identical to rev/s (1 Hz = 1 rev/s = 60 RPM = 2π rad/s) but more common in physics, vibration analysis, and rotor-dynamics contexts where the frequency-domain interpretation matters. Used in: rotor-dynamics critical-speed studies per API 684 and ISO 21940 (the first-bending-mode critical speed of a 200 MW steam turbine rotor is typically 25-35 Hz, well separated from the 50/60 Hz grid synchronous speed at 50/60 Hz exactly), NDT (Non-Destructive Testing) vibration surveys per ISO 10816, FFT spectral analysis of rotating-machinery vibration signatures (the 1× = running speed peak, 2× = misalignment, 3-10× = blade-pass or gear-mesh frequencies depending on machine type), and balancing-machine output per ISO 1940 / ISO 21940-11. NOT to be confused with Hz as an electrical / temporal / oscillatory frequency (though they share the same underlying '1/s' dimension and are sometimes deliberately conflated in spectral analysis).

It belongs to the metric measurement system.

Hertz (rotational) are commonly used in motor specifications, rotating machinery, and mechanical design.