[BerntR]

Bernt
The fact that the object is changing direction means that there is a force present that is causing that change of direction. If a force is present and causing a change in the direction of the object's path, then it is doing work by moving the object in another direction.

Jeff,

d Work/dt (work per time unit, power) = A * B * cos(ab),

A = centripetal force,
B = distance per time unit (speed),

ab = angle between force and speed = 90*
cos(ab) = Zero.

Work per time unit is zero at all times as far as the centripetal force is conserned. Therefore total work is zero.

All this is according to Newton's physics.