Physics - Kinematics - Angular Velocity ()

By: nobody ( Nobody/Anonymous )
w x r  
2004-01-30 22:26

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So differentiating both sides with respect to time and representing in vector notation with perpendicualr to both and ( is into paper)

= x

Where:

is the instantaneous angular velocity about . = d/dt (units radians / sec)
x is the cross product operator (see here for definition)
is the instantaneous position of the particle relative to point. - (units meters)
is the instantaneous linear velocity (units meters / sec)
So the rotation velocity of a point is not an absolute value, but it depends on which point that the rotation is measured about. Also the particle does not have to be traveling in a circle to have an angular velocity, it can have a non-zero angular velocity about , even if the particle is traveling in a straight line, provided is not on the line.
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the above is a line form this web site. In it it mentions that v= r x w. I might be reading the symbols wrong, but the equation for the tangential velocity is usually v=w x r, from the right hand rule.

By: martinbaker ( Martin Baker )
RE: w x r  
2004-01-31 10:53

OK, thanks for letting me know about this.

Andy sent me a file showing that some of my maths pages were inconsistent, I have been working through this and I think the reason is that some pages have used right hand coordinates and some have used left hand coordinates.

From your message it looks like I need to check the physics pages as well.

I have decided to use the right hand coordinate system and also the right hand rule for angles, this is because it is used by VRML/x3d standards.

In these standards:
+X is right.
+Y is up
+Z is out of screen (toward viewer)
+angles are as given by right hand rule.

Unfortunately it will take me some time to work though the site to make all pages consistent, but it is important.

Thanks,

Martin