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forum Forum index forumQM forumAngular velocity

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Author : Topic: Angular velocity  Bottom
 saucer
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 A Good Tautology is Hard to Find!
 saucer
  Posted 08/08/2007 09:26:43 PM
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....A single number which has no direction is either a scalar or a pseudoscalar, the difference being that a scalar does not change its sign when the x  and y  axes are exchanged (or inverted), while a pseudoscalar does. The angle as well as the angular velocity is a pseudoscalar. The positive direction of rotation is taken, by convention, to be in the direction towards the y  axis from the x axis. If the axes are inverted, but the sense of a rotation does not, then the sign of the angle of rotation, and therefore the angular velocity as well, will change.

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--Last edited by saucer on 2007-08-08 21:31:10 --

 saucer
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 A Good Tautology is Hard to Find!
 saucer
  Posted 08/08/2007 09:33:37 PM
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It is an important point that the spin angular velocity of every particle in the rigid body is the same, and that the spin angular velocity is independent of the choice of the origin of the rigid body system or of the lab system. In other words, it is a physically real quantity which is a property of the rigid body, independent of one's choice of coordinate system. The angular velocity of the reference point about the origin of the lab frame will, however, depend on these choices of coordinate system. It is often convenient to choose the center of mass of the rigid body as the origin of the rigid body system, since a considerable mathematical simplification occurs in the expression for the angular momentum of the rigid body..



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 saucer
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 A Good Tautology is Hard to Find!
 saucer
  Posted 08/08/2007 09:41:39 PM
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   ω is the angular frequency or angular speed (measured in radians per second),
   T is the period (measured in seconds),
   f is the frequency (measured in hertz),
   v is the tangential velocity of a point about the axis of rotation (measured in metres per second),
   r is the radius of rotation (measured in metres).

Angular frequency is therefore a simple multiple of ordinary frequency. However, using angular frequency is often preferable in many applications, as it avoids the excessive appearance of π. In fact, it is used in many fields of physics involving periodic phenomena, such as quantum mechanics and electrodynamics.


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