Properties Of A Plain Area
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Properties Of A Plain Area Consider figure 124.1:
(a) Where is the centroid of the plane area?
(b) Write the general expression for the moment of inertia about the x axis
(c) Write the general expression for the moment of inertia about the y axis
(d) Write the general expression for the polar moment of inertia
(e) Write the general expression for the product of inertia
(f) Write the general expression for the radius of gyration with respect to the x axis
(g) Write the genaral expression for the radius of gyration with respect to the y axis
(h) Show that the polar moment of inertia is the sum of the moment of inertia about the x axis and the moment of inertia about the y axis.

The strings: S7P2A21 (Identity - Physical Properties).

The math:
Pj Problem of Interest is of type identity (physical properties). (a) Centroid is at G, the intersection of the lines m and l.

(b) Moment of inertia about x = Ix = ∫dA(x2).

(c) Moment of inertia about y = Iy = ∫dA(y2).

(d) Polar Moment of inertia = Jz = ∫dA(r2).
Where r, is the distance from O to dA.

(e) Product of inertia = Hxy = ∫dA(xy).

(f) Radius of gyration = kx = √(Ix/Area)

(g) Radius of gyration = ky = √(Iy/Area)

(h) Ix + Iy = ∫dA(x2) + ∫dA(y2).
So, Ix + Iy = ∫dA[x2 + y2] = ∫dA(r2) = Jz.

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Composition And Structure Of Matter
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How Matter Gets Composed (2)
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