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Find the motion of inertia of helical wire.

Find the motion of inertia of helical wire.

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1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
9 years ago
Consider a wire in the shape of a helix r(t)=4costi+4sintj+7tk, 0<(or =) t <(or =)2 with constant density function (x,y,z)=1 .

Find the moment of inertia about the z-axis?
This equals ?c (x^2 + y^2) d(x,y,z) ds
= ? (x^2 + y^2) * 1 * ||r'(t)|| dt
= ?(t = 0 to 2) ((4 cos t)^2 + (4 sin t)^2) * v((-4 sin t)^2 + (4 cos t)^2 + 7^2) dt
= ?(t = 0 to 2) 16v65 dt
= 32v65.

I hope this helps!
Thannks & Regards
RInkoo Gupta
ASkIITians Faculty

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