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assignment 32 soln

# assignment 32 soln - {k PROBLEM 9.19 t x" T Determine...

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Unformatted text preview: !/ {k PROBLEM 9.19 t x" _. T Determine the moment of inertia and the radius of gyration of the shaded , ' /\ 3:13 1’ area shown with respect to the x axis. .r’l K" / I; = 0 Lu kr \\ x ' \5 SOLUTION First note: At x z 0: b = c cos(0) or c = b At x = 2a: b = bsink(Za) or 2ka= E 2 k = 3”— 4a Then A = [3"[bsm4—‘Zx — bcosixjdx ( 4a 7: 4a . Jr )2“ = b ——cos—x — —sm—x 7: 4a 7: 4a a 4ab l l = — 1 — ~— + —‘ 7r [( ) [ﬂ ﬂ” = 1% — 1) 7: Have 1x = Jysz 2 bsin x = I: bmsgxysz’dx 4a = éffibssrf n x — bscoss—Exjdx - b3 [—ﬂcoslx + liqcos3£xj — [ﬂsinlx — lﬂsin31x) 71: 4a 3 7: 4a 3 4a =ifit-l+%1-[-%+%(%J3was} And ,ﬁ; 97: PROBLEM 9.19 CONTINUED ab3(5J§ — 4) = 0 21m»3 N I x 7 1,r = 0.217611;3 4 IQ. = 0.64212 4 PROBLEM 9.10 Determine by direct integration the moment of inertia of the shaded area with respect to the x axis. SOLUTION At or Then I = g); b i or y = 1 x3 (2a)?— 3 Now de=ly3dx=—1-b— 3 3 2a 3 3 20 Then 1x=Jd1x=lb—20xdx=lb—lxz ' 32a " 6 a 2 '1 b3 2 2 :5 m(4a — (1 ) ...
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assignment 32 soln - {k PROBLEM 9.19 t x" T Determine...

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