if it is making stepping clicks at 12 or 16 steps per rotation, it could be a rotary encoder.
otherwise it is a resistive potentiometer. once the rotation is found smooth you can find out the total value of the pot , by measuring resistance across outer pins .
then wrt to one side , you could measure with one end of rotation indicating full value as measured earlier. now,rotate by 1/3rd of the 300 odd degrees possible, measure. then rotate another 1/3rd, if the measurements are proportionate approximately, then it is linear one, otherwise logarithmic one. in general volume controls that manage audio are logarithmic.
ps:
a rotary encoder rotates continuously with no end stops .