On 9 Oct 2003 05:44:20 -0700, jim rozen wrote:
But for a pendulum, the displacement
and the force are still orthogonal.

No it isn't. The pendulum swings down
and in, or up and out. The up and down
components are in line with the force.
So work is done in each half of the
swing. It is just that the positive work
while the pendulum is swinging down
is offset by the negative work done
as the pendulum is swinging up. So
net work is zero.

The dot product is still zero.

Depends on over what part of the swing you calculate
it. If you picture the pendulum end points as a and c,
and call the midpoint b. Then from a to b positive work
is done, and from b to c negative work is done. If you
calculate directly from a to c, of course, the result is
zero. That's because you're adding the work done in
the two halves of the swing together.

Wac = Wab + (- Wbc)

Since, ignoring friction, Wab and Wbc have the same
magnitudes, but opposite signs, Wac should always
equal zero.

Gary