Why is it that Angular Velocity of a body about any point the same ?
Eg: If a rod hinged at one end rotates with an angular velocity W the angular velocity about its center is also W.
Also is it true for points out of the body ??
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Angular velocity is a manifestation of the change of orientation. In a rigid body, every point on the body has the same orientation and thus shares rotational motion. See link above since this question has been asked before. – John Alexiou Jan 04 '15 at 16:40
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Angular velocity is pseudo-vector whose magnitude measures the rate of change of an angle with time. If a point is rotating on the horizontal plane at a fixed distance $r$ from a fixed axis, and with tangential speed $v$, say anticlockwise, the angular velocity is a vector pointing up vertically and whose magnitude is the ratio $v/r$. Now the trajectory is a circle and therefore the distance travelled is $d = vt$. Since $d$ is an arc of a circumference, its ratio to the radius $r$ is the measure of an angle in radians, hence $d/r = vt/r$ is an angle, and therefore $\dot d = v/r$ is the angular speed, which is now independent on the radius.
Phoenix87
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