Rotational speed (sometimes called speed of revolution) is the number of complete rotations, revolutions, cycles, or turns per time unit. Rotational speed is a cyclic frequency, measured in radians per second or in hertz in the SI System by scientists, or in revolutions per minute (rpm or min-1) or revolutions per second in everyday life. The symbol for rotational speed is ω (the Greek lowercase letter "omega").
When proper units are used for tangential speed v, rotational speed ω, and radial distance r, the direct proportion of v to both r and ω becomes the exact equation:
In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector is sometimes used as a synonym for the vector quantity angular velocity.
One revolution is equal to 2π radians, hence
Rotation around a fixed axis is a special case of rotational motion. The fixed axis hypothesis excludes the possibility of an axis changing its orientation, and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation around more than one axis at the same time is impossible. If two rotations are forced at the same time, a new axis of rotation will appear.
This article assumes that the rotation is also stable, such that no torque is required to keep it going. The kinematics and dynamics of rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; they are entirely analogous to those of linear motion along a single fixed direction, which is not true for free rotation of a rigid body. The expressions for the kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational motion. For these reasons, rotation around a fixed axis is typically taught in introductory physics courses after students have mastered linear motion; the full generality of rotational motion is not usually taught in introductory physics classes.
A physical quantity (or "physical magnitude") is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.
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