(a) Explanation Calculation: Consider the regular pentagon shown, with centroid axes x and y . Sketch the regular pentagon as shown in Figure 1. The y axis is an axis of symmetry. It is expressed as follows: I x y = 0 The x and y axes must be principle axes in case of axis of symmetry. I x = I max I y = I min Sketch the Mohr’s circle as shown in figure 2. The axes are rotated through angle α and the moment of inertia I x ′ y ′ . For symmetry I x ′ y ′ = 0 (b) To determine Show that the product of inertia with respect to every pair to rectangular axes through the centroid is zero.

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ISBN: 9781259977268

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 9.4, Problem 9.108P

(a)

To determine

Show that the moment of inertia with respect to every axis through the centroid is the same.

(b)

To determine

Show that the product of inertia with respect to every pair to rectangular axes through the centroid is zero.

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Chapter 9.4, Problem 9.107P

Chapter 9.4, Problem 9.109P

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Show that the moment of inertia with respect to every axis through the centroid is the same.

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Show that the moment of inertia with respect to every axis through the centroid is the same.

Show that the product of inertia with respect to every pair to rectangular axes through the centroid is zero.

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