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Rotational frequency, also known as rotational speed or rate of rotation (symbols ν, lowercase Greek nu, and also n), is the frequency of rotation of an object around an axis. Its SI unit is the reciprocal seconds (s −1 ); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).
The angular momentum equation can be used to relate the moment of the resultant force on a body about an axis (sometimes called torque), and the rate of rotation about that axis. Torque and angular momentum are related according to =, just as F = dp/dt in linear dynamics. In the absence of an external torque, the angular momentum of a body ...
For example, if a person places a force of 10 N at the terminal end of a wrench that is 0.5 m long (or a force of 10 N acting 0.5 m from the twist point of a wrench of any length), the torque will be 5 N⋅m – assuming that the person moves the wrench by applying force in the plane of movement and perpendicular to the wrench.
In physics, angular velocity (symbol ω or , the lowercase Greek letter omega), also known as the angular frequency vector, [1] is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler.
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).
For free-floating (unattached) objects, the axis of rotation is commonly around its center of mass. Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion: E translational = 1 2 m v 2 {\displaystyle E_{\text{translational}}={\tfrac {1}{2}}mv^{2}}
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 =. This comes from the following: the linear (tangential) velocity of an object in rotation is the rate at which it covers the circumference's length: