# Is force always the negative change in potential energy with respect to position?

For example, In the non-inertial rotating reference frame of a turntable that has a tether ball pole rotating on top of it, the ball at the end instantly starts rotating and then eventually moves up to its final orbit radius and height. We should be able to define a potential caused by the centrifugal force and gravity. Because of the constraint of the length of the string and constant angular velocity this potential can be written in terms of just height. Would differentiating the potential with respect to height yield some sort of force?

• Can a velocity dependent force, e.g., the force due to a dashpot, be proportional to the spatial rate of change of a potential? – Alfred Centauri May 25 at 22:56