# Equation of constraint - Falling disc unrolling from an attached string

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!

• The angle increases continuously through $2\pi, \, 4\pi, \, 6\pi \, …$ etc. – 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 $$y$$.