If a wire with linear density ρ(x, y, z) lies along a space curve C, its moments of inertia about the x-, y-, and z-axes are defined as
Ix = ∫C (y2 + z2) ρ(x, y, z) ds
Iy = ∫C (x2 + z2) ρ(x, y, z) ds
Iz = ∫C (x2 + y2) ρ(x, y, z) ds
Find the moments of inertia for the wire in Exercise 35.
35. (a) Write the formulas similar to Equations 4 for the center of mass (
(b) Find the center of mass of a wire in the shape of the helix x = 2 sin t, y = 2 cos t, z = 3t, 0 ⩽ t ⩽ 2π, if the density is a constant k.
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