At the instant shown, the spring is undeformed. Determine the change in potential energy if the $20$ $kg$ disk ($k_g = 0.5$ $m$) rolls 2 revolutions without slipping. Note that the shown velocity vector refers to the translation of the centre of the wheel.

A. $\frac{1} {2} (200)(1.2\pi)^2 + (20)9.81(1.2\pi \sin(30))$
B. $- \frac{1} {2} (200) (1.2\pi)^2 - (20)9.81(1.2\pi \sin(30))$
C. $\frac{1} {2} (200)(1.2\pi)^2 - (20)9.81(1.2\pi \sin(30))$
D. $\frac{1} {2} (200)(1.2\pi)^2$