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

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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 64E
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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.

Review your line integral skills: Consider a wire in the shape of a helix r(t) = 7 cos ti + 7 sin tj + 4tk, 0 <t< 2n with constant density function p(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 p(x, y, z) lies along a space curve C, its moment of inertia about the z-axis is defined by I, = Sc(r² + y²)p(x, y, z)ds.
Transcribed Image Text:Review your line integral skills: Consider a wire in the shape of a helix r(t) = 7 cos ti + 7 sin tj + 4tk, 0 <t< 2n with constant density function p(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 p(x, y, z) lies along a space curve C, its moment of inertia about the z-axis is defined by I, = Sc(r² + y²)p(x, y, z)ds.
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