Rotationsrate

Rotationsrate, or rotation rate, is the rate at which an object turns around an axis. In physics, the instantaneous rotation rate is the magnitude of the angular velocity, often denoted |ω|, while the angular velocity vector ω has both magnitude and direction (the direction given by the right-hand rule). The rotation rate is typically measured in radians per second (rad/s) in the SI system, but revolutions per minute (RPM) or degrees per second are also common in engineering.

The rotation rate relates to angular velocity by ω = |ω|, with the vector direction indicating the rotation axis. The rotation rate can be related to frequency by f = ω/(2π), and conversely ω = 2πf. For circular motion, the tangential speed v is v = rω, where r is the radius from the axis. If the rotation rate is constant, angular displacement is θ = ωt; if it varies, θ = ∫ ω dt, and angular acceleration is α = dω/dt.

Measurement and observables vary by context. In mechanical systems, rotation rate is measured with tachometers or encoders and monitored by control systems. In astronomy, rotation rates of planets and stars are inferred from periodic signals, spectral line broadening, or Doppler shifts. In geology and geodesy, Earth’s rotation rate is known as approximately 7.2921159×10^-5 rad/s, corresponding to a sidereal day of about 86164 seconds.

Rotationsrate is a foundational quantity in dynamics and kinematics, underpinning analyses of gears, turbines, gyroscopes, robotics, and celestial mechanics. It distinguishes from angular velocity by focusing on the rate of rotation’s magnitude, while the vector form provides the axis and sense of rotation.