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In physics, angular velocity (symbol ω or , the lowercase Greek letter omega), also known as 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.
A diagram of angular momentum. Showing angular velocity (Scalar) and radius. In physics, angular mechanics is a field of mechanics which studies rotational movement. It studies things such as angular momentum, angular velocity, and torque. It also studies more advanced things such as Coriolis force [1] and Angular aerodynamics.
Angular momenta of a classical object. Left: intrinsic "spin" angular momentum S is really orbital angular momentum of the object at every point, right: extrinsic orbital angular momentum L about an axis, top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω) [6] bottom: momentum p and its radial position r ...
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).
where is the mass of the rigid body; ¯ is the velocity of the center of mass of the rigid body, as viewed by an observer fixed in an inertial frame N; ¯ is the angular momentum of the rigid body about the center of mass, also taken in the inertial frame N; and is the angular velocity of the rigid body R relative to the inertial frame N. [3]
where M k are the components of the applied torques, I k are the principal moments of inertia and ω k are the components of the angular velocity. In the absence of applied torques, one obtains the Euler top. When the torques are due to gravity, there are special cases when the motion of the top is integrable.
For amplitudes beyond the small angle approximation, one can compute the exact period by first inverting the equation for the angular velocity obtained from the energy method , = and then integrating over one complete cycle, = (), or twice the half-cycle = (), or four times the quarter-cycle = (), which leads to = .
Likewise, the momentum vector is the velocity vector (a polar vector) times mass (a scalar), so is a polar vector. Angular momentum is the cross product of a displacement (a polar vector) and momentum (a polar vector), and is therefore a pseudovector. Torque is angular momentum (a pseudovector) divided by time (a scalar), so is also a pseudovector.