(a) Explanation Calculation: Sketch the cone as shown in Figure 1. Refer to problem 9.11 in the textbook. Express the moment of inertia of cone about x axis. I x = 3 10 m a 2 (1) Express the moment of inertia of cone about y and z axis. I y = I z = 3 5 m ( 1 4 a 2 + h 2 ) (2) The product of inertia about I x y , I y z , I z x is 0, due to symmetry of corresponding axes. It is expressed as follows: I x y = 0 I y z = 0 I z x = 0 Refer to Equation 9.48 in the textbook. Express the Equation of ellipsoid of inertia as follows: I x x 2 + I x y 2 + I z z 2 = 1 3 10 m a 2 x 2 + 3 5 m ( 1 4 a 2 + h 2 ) y 2 (b) To determine Find the value of ratio a / h such that ellipsoid of inertia of the cone is sphere when computed at the center of base of the cone.

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 9.6, Problem 9.175P

(a)

To determine

Find the value of ratio a/h such that ellipsoid of inertia of the cone is sphere when computed at the apex of the cone is 2.

(b)

To determine

Find the value of ratio a/h such that ellipsoid of inertia of the cone is sphere when computed at the center of base of the cone.

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Chapter 9.6, Problem 9.174P

Chapter 9.6, Problem 9.176P

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Chapter 9 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - Prob. 9.3P Ch. 9.1 - Prob. 9.4P Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - Prob. 9.7P Ch. 9.1 - Prob. 9.8P Ch. 9.1 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - Prob. 9.10P

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Find the value of ratio a / h such that ellipsoid of inertia of the cone is sphere when computed at the apex of the cone is 2.

Solution Summary: The author explains how to calculate the ellipsoid of inertia of the cone.