Consider a wire in the shape of a helix $r(t) = 7 \cos t \mathbf{i} + 7 \sin t \mathbf{j} + 3t \mathbf{k}$, $0 \le t \le 2\pi$ with constant density function $\rho(x, y, z) = 1$.
A. Determine the mass of the wire:
B. Determine the coordinates of the center of mass: (
C. Determine the moment of inertia about the $z$-axis:
)
Recall that the mass of the wire is $m = \int_C \rho \, ds$, the moments about the $xy$, $yz$, and $xz$ planes are $M_{xy} = \int_C \rho z \, ds$, $M_{yz} = \int_C \rho x \, ds$, and $M_{xz} = \int_C \rho y \, ds$, and the moment of inertia about the $z$-axis is $M_z = \int_C \rho (x^2 + y^2) \, ds$.
