Learning Goal:
To be able to compute moments of inertia using calculus.
To analyze or design a structural member or a mechanical part,
the moment of inertia for the cross-sectional area of the member
must be known. For example, when studying how beams bend,
the moment of inertia for the cross-sectional area of the beam
plays an important role in determining both the stresses in the
beam and the deflection of the beam. In the figure shown below
(Figure 1), an elemental area is selected, and then integration is
performed to obtain the moment of inertia for the entire surface.
The entire area's moment of inertia about the x axis is given by
$I_x = \int_A y^2 dA$
and the moment of inertia about the y axis is given by
$I_y = \int_A x^2 dA$
Part A - Moment of inertia about the x axis
Determine the moment of inertia with respect to the x axis for the shaded area shown (Figure 2). The dimension is a = 3.00 m.
Express your answer to three significant figures and include the appropriate units.
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$I_x = $
Value
Units
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Figure
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