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The radian per second (symbol: rad⋅s −1 or rad/s) is the unit of angular velocity in the International System of Units (SI). The radian per second is also the SI unit of angular frequency (symbol ω, omega). The radian per second is defined as the angular frequency that results in the angular displacement increasing by one radian every ...
= 1 Hz = 1/s radian per second: rad/s ≡ 1/(2π) Hz ≈ 0.159 155 Hz: revolution per minute: rpm ≡ One rpm equals one rotation completed around a fixed axis in one minute of time. ≈ 0.104 719 755 rad/s
A sphere rotating around an axis. Points farther from the axis move faster, satisfying ω = v / r.. In physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves).
The SI unit of angular velocity is radians per second, [3] although degrees per second (°/s) is also common. The radian is a dimensionless quantity , thus the SI units of angular velocity are dimensionally equivalent to reciprocal seconds , s −1 , although rad/s is preferable to avoid confusion with rotation velocity in units of hertz (also ...
is the motor velocity, or motor speed, [2] constant (not to be confused with kV, the symbol for kilovolt), measured in revolutions per minute (RPM) per volt or radians per volt second, rad/V·s: [3]
One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.
Its angular frequency is 360 degrees per second (360°/s), or 2π radians per second (2π rad/s), while the rotational frequency is 60 rpm. Rotational frequency is not to be confused with tangential speed, despite some relation between the two concepts. Imagine a merry-go-round with a constant rate of rotation.
Thus a disc rotating at 60 rpm is said to have an angular speed of 2π rad/s and a rotation frequency of 1 Hz. The International System of Units (SI) does not recognize rpm as a unit. It defines units of angular frequency and angular velocity as rad s −1, and units of frequency as Hz, equal to s −1.