Thanks very much for this.
The
reason that I've got clockwise motion as positive is that I have
tried to standardise on:
1) a left hand coordinate
system (+x to right, +y up and +z toward viewer).
2)
left hand rule for rotation (left thumb points in positive
direction of axis of rotation, curl of fingers gives
rotation).
So if we are considering rotation
about the z-axis and if our left hand thumb points in the
positive z-direction (toward viewer) then the fingers curl in a
clockwise direction.
However, if we choose a
right hand rule for both coordinate and rotation (right thumb
away from viewer) then we also get positive clockwise
rotation.
Its only if we choose left hand
coordinates with right hand rotation, or visa versa, that we get
anticlockwise rotation as positive.
I agree
that anticlockwise rotation is usually shown as positive, but I
keep finding cases of conflicting standards and conventions in
this subject, I guess that's what makes it so hard (or should I
say such an interesting challenge) to work out.
I
think your right about using r x J instead of J x r, because the
corresponding torque equation is usually r x F, although I think
I've seen it the other way round. I guess I could just change it
and make everything fit but having got to this stage I would
really like to clarify these issues.
I guess
we need to go back to the equations:
angular momentum of
a particle = L = r x p
torque = T = F x r (or rotational
impulse = J x r)
and find out if they are defined for
left or right hand coordinates and left or right hand
rotations?
The vector 'x' product itself must
have some left-or-right-handed-ness because we arbitrarily choose
a direction for the result, we could just as easily chosen the
other direction for the result of a cross product.
I'm
not quite sure how to take this forward? I would like the site to
clarify exactly what standards and conventions are being
assumed.
I'll have to think about this a bit
more I would welcome any more ideas.
cheers,
Martin |
