Physics - Kinematics - Angular Velocity ()

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

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

= x


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.
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 )
file 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.



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