Helix Moment

\[ x = \cos \theta , \qquad y = \sin \theta, \qquad z = \theta, \qquad 0 \leq \theta \leq 2 \pi \]

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.

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