Helix MomentClassical Mechanics Level 2
\[ x = \cos \theta , \qquad y = \sin \theta, \qquad z = \theta, \qquad 0 \leq \theta \leq 2 \pi \]
Consider a helical section, with parameters given above. The mass of the helical section is \(M\). The moment of inertia about the \(z\)-axis can be expressed as \(\alpha M\). Determine the value of \(\alpha\).
Details and Assumptions:
- The mass is distributed uniformly as a function of arc length.
- Neglect units.