
Concept explainers
(a)
Find the mass moment of inertia
(a)

Answer to Problem 9.118P
The mass moment of inertia
Explanation of Solution
Given information:
The height of the section is 1.5a.
The width of the section is a.
The length of the section up to straight edge is 2a.
The length of the section in sloped edge is 2a.
Calculation:
Let divide the section into 1 and 2.
Show the section 1 and section 2 as in Figure 1.
Calculate the area
Calculate the area
Calculate the value
Substitute
Calculate the value
Substitute
Calculate the value
Substitute
Calculate the value
Substitute
Calculate the centroid
Substitute
Calculate the centroid
Substitute
Calculate the area (A) of the trapezoidal plate as below:
Express the mass (m) as below:
Here,
Rewrite the above equation as,
Substitute
Express the mass moment of inertia
Substitute
Calculate the moment of inertia of area
Calculate the moment of inertia of area
Calculate the moment of inertia
Substitute
Calculate the mass moment of inertia
Rewrite the equation (1) as,
Substitute
Calculate the moment of inertia of area
Calculate the centroid
Express the moment of inertia
Calculate moment of inertia of area
Substitute
Calculate the moment of inertia
Substitute
Calculate the mass moment of inertia
Rewrite the equation (1) as,
Substitute
Calculate the mass moment of inertia
Substitute
Write the expression for mass moment of inertia
Rewrite the above equation as,
Calculate the mass moment of inertia
Substitute
Therefore, the mass moment of inertia
(b)
The mass moment of inertia
(b)

Answer to Problem 9.118P
The mass moment of inertia
Explanation of Solution
Given information:
The height of the section is 1.5a.
The width of the section is a.
The length of the section up to straight edge is 2a.
The length of the section in sloped edge is 2a.
Calculation:
Write the expression for mass moment of inertia
Calculate the mass moment of inertia
Substitute
Substitute
Therefore, the mass moment of inertia
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Chapter 9 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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