Moments of Inertia I

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Moments of Inertia I (Second moment of the Area)
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In the previos chapter ((centroid)) , W
A ? dA and ? ydA wem found and
calcnlated. Sometimes, F maynitude dpends on
A as well as the distance fram A to som givem
axis.

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F Ry A The resn ltant R of the fores
F ans the entine cross-section is R ? F
? ky dA k ?A ydA
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? y dA y A frist moment of the
cross-sectioned anse about the x-axix
0 (since the centurion is locaed
on the x-axis.)
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The moment about the x-axix Mx ( F) y
(ky A)y k
A Mx ? Mx ?A k dA
K ?A dA
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? dA moment of inertia (or second moment
of the cros-section arce) wrt to the x-axis
Ix always
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Ix ? dA
units Iy ? dA
(e.g. , , .etc) Ix and
Iy can be determined by integration. Theis is
pune math as, yon can see the hand out.
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Polar moment of inertia Jo J0 ? dA J0
is the polar moment of inertia of A wrt 0. J0
? dA ? ( ) dA ? dA
? dA J0 Ix Iy
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Radius of gyration k Kx Ky Ko
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