Concept explainers
Determine the mass moment of inertia of the steel fixture shown with respect to (a) the x axis, (b) the y axis, (c) the z axis. (The density of steel is 7850 kg/m3.)
Fig. P9.145
(a)
Find the mass moment of inertia with respect to x axis.
Answer to Problem 9.145P
The mass moment of inertia with respect to x axis is
Explanation of Solution
Given information:
The density
Calculation:
Sketch the section of steel fixture as shown in Figure 1.
Find the mass
Here, V is volume of rectangular section 1.
Modify Equation (1).
Here, w is the width of the section 1, l is the length of the rectangular section 1, and t is the thickness of the section 1.
Substitute
Find the mass
Here, V is volume of rectangular section 2.
Modify Equation (3).
Here, w is the width of the section 2, l is the length of the rectangular section 2, and t is the thickness of the section 2.
Substitute
Find the mass
Substitute
Refer to Figure 9.28, “Mass moment of inertia for common geometric shapes” in the text book.
Find the mass moment of inertia with respect to x axis as shown below:
Convert the dimension in mm to m.
Similarly calculate the remaining values.
Substitute
Thus, the mass moment of inertia with respect to x axis is
(b)
Find the mass moment of inertia with respect to y axis.
Answer to Problem 9.145P
The mass moment of inertia with respect to y axis is
Explanation of Solution
Calculation:
Find the mass moment of inertia with respect to y axis as shown below:
Convert the dimensions in mm to m.
Substitute
(c)
Find the mass moment of inertia with respect to z axis.
Answer to Problem 9.145P
The mass moment of inertia with respect to z axis is
Explanation of Solution
Calculation:
Find the mass moment of inertia with respect to z axis as shown below:
Convert the dimensions in mm to m.
Substitute
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Chapter 9 Solutions
Vector Mechanics for Engineers: Statics
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