Where does the equation of constraint below come from? I've tried to rationalize it, but the angle will be 0 more than one time as the string unrolls, even though y will keep going down (right?), not coming back to 0 (y=0 is considered to be at the point of suspension). I'd appreciate any help, thanks!

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    $\begingroup$ The angle increases continuously through $2\pi, \, 4\pi, \, 6\pi \, …$ etc. $\endgroup$ – Farcher Apr 4 at 13:31

The angle is $0$ only when $y=0$ at the point of suspension. It keeps on increasing thereafter, although the multiples of $2\pi$ correspond to the same point on the disc.

The equation $y = a\phi$ is just identifying the arc length as the vertical distance $y$.

  • $\begingroup$ Wow am I dumb! For some reason I was thinking as if it was cos or sin, where it would cyclically return to zero. It is just the angle though... Thanks for clearing my muddy mind! $\endgroup$ – iSkillzPT Apr 4 at 18:56

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