   Chapter 16.7, Problem 41E

Chapter
Section
Textbook Problem

(a) Give an integral expression for the moment of inertia I about the z-axis of a thin sheet in the shape of a surface S if the density function is ρ.(b) Find the moment of inertia about the z-axis of the funnel in Exercise 40.

(a)

To determine

To find: The integral expression for the moment of inertia Iz about the z -axis.

Explanation

Formula used:

m=Sρ(x,y,z)dS (1)

As the moment of integration is about the z -axis that is z=x2+y2 .

Modify equation (1).

Iz=Szρ(x,y,z)dS

Substitute x2+y2 for z ,

(b)

To determine

To find: The moment of inertia about z -axis of the funnel.

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