Chapter 15.4, Problem 20E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Consider a square fan blade with sides of length 2 and the lower left comer placed at the origin. If the density of the blade is *ρ* (*x, y*) = 1 + 0.1*x,* is it more difficult to rotate the blade about the *x*-axis or the *y*-axis?

To determine

The direction of the fan blade in which it is more difficult to rotate.

Explanation

**Given:**

The region *D* is *xy* plane occupied by the fan bladewith sides of length 2*.*

The density function

**Formula used:**

The moments of inertia is,

Here, the density function is given by
*D* is the region that is occupied by the lamina.

**Calculation:**

From the given conditions it is observed that *x* varies from 0 to 2 and *y* varies from 0 to 2. Obtain the direction of the fan blade in which it is difficult to rotate by find the moments of inertia about *x* and *y* axes.

Obtain the moment of inertia

Integrate with respect to *y* and apply the corresponding limit.

Integrate with respect to *x* and apply the corresponding limit.

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