Say you have a spiral helical spring, like one you might find in a wind-up toy or a hairspring in a watch. The center is attached to a rod that can be twisted to wind it, and the outer end of the spring is permanently fixed to something.
I am trying to calculate the restoring force exerted by the spring, and I believe force applied is the force required to turn the rod attached to the center of the spring. But how should I measure the displacement of the spring?
Another application of Hooke's law that I am unsure of on a spiral helical spring is calculating force applied without an initial measurement. To obtain the Force applied using Hooke's law, I would need the stiffness (k) of the said spring. And unfortunately to find k, I would need to know the force applied. In this sense, I find myself unable to measure the force applied on the said spring without having an initial measurement of force, say 5N. Thus, without somehow measuring exactly how many Newtons of rotational force I exert to turn the rod with my fingers, for example.