Sliding Down a Helix

A bead slides from rest down a wire that's bent into a helix, which can be parametrized in the following way: {x=cos(θ)y=sin(θ)z=θ. \begin{cases} x = \cos(\theta) \\ y = \sin(\theta) \\ z = \theta. \end{cases} Find the magnitude of the bead's vertical acceleration.


Assumptions: The bead slides without friction and there is a uniform, gravitational field gz^.-g\,\hat{\mathbf{z}}.

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