A rolling disc from a slope also has the same expressions. I guess it shouldn't be the coincidance since the initial energy is shared by linear motion and rotational motion in the same way.
Calculate the center of rotation? Of mass? There is no center. Its pushed directly right angles to the center of rotation like an axle would be creating horizontal rotational torque
Great explanation! There’s one thing I don’t understand, what happens with the Work (T*h) the tension gives? Shouldn’t this be in the conservation of energy formula?