Answered: Review your line integral skills:…

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Review your line integral skills: Consider a wire in the shape of a helix r(t)=7costi+7sintj+4

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.5: Applications

Problem 19EQ

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Question

8.2

Review your line integral skills: Consider a wire in the shape of a helix r(t)=7costi+7sintj+4tk,0≤t≤2πr(t)=7cos⁡ti+7sin⁡tj+4tk,0≤t≤2π with constant density function ρ(x,y,z)=1ρ(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:
Note: If a wire with linear density ρ(x,y,z)ρ(x,y,z) lies along a space curve CC, its moment of inertia about the z-axis is defined by Iz=∫C(x2+y2)ρ(x,y,z)dsIz=∫C(x2+y2)ρ(x,y,z)ds.