Beer, Johnston, Eisenberg Vector Mechanics for Engineers – Statics 8 ed Ch9_2007

# Vector Mechanics for Engineers: Statics w/CD-ROM

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PROBLEM 9.11 Determine by direct integration the moment of inertia of the shaded area with respect to the.r axis. / - r ( ( , - e b \ : b : 4 K : ,r(r-.-9 b > .i- c o t-' la , l , 6 rr,a = f Z,ro ."t--P {" \,L,e-€- **J'n" :rx = [ ['t' rb J^ = t"- [ *' LlJ-.f f(*"t 3o e-\ - ZoJ'o j * ;) 3 ( l^ e-t) D .--,1 ( ao. - \,5a ., *41 O. tto+ o. t3

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*#*-ff; PR,OBLEM 9.23 Deterrnine tlie polar moment of inertia and the polar radius of gyration of the shaded arrca shown with respect to point P. \r=;! ^'*u = *(rr**) h = l(*,-rJdx = f- L5 (^+..) - * la^ b 3 t ; - , : s F K * a - x v& , bo7 = - * - s & f t 4 : = Y * z + c 0 ' o - \ 7 < = 9 q - b = C , o a \ > = e q = L L 4 2 V = K a z + b ,. zv-b t a = c , . t = ; ? b ? E X - V 6 bh3 ]fx =-T %' = rvrX q\ x= * , ,1=?.t zV rq= E zt f , t = E x l * I I l o b a =. ? - q @\ '"tb* .3bc- _ 3tc^ - s ' 3 \,1- t= dx ^=X a \ 8 t 3 c ^ ) - F =..s f"Ali - *tl)a- J o \ =i(" S (*'*o3)=- #*')l^ = f f* 63 (*.* 3c^..xq + 3o.{ \t + = ) o ; =*[* x?+#5-'*#f x t J
+€ oo a' r 3 + b q . .S "..] T! = J*'dA = f :^= [* C^.+^.') - +*] +^ = J,"@. x{ + bx'- [ - u s t F*=**o'-+ , u J3 bL3 't':. --+ 3 * n) r,. l I . . Y 1( = o\ ? b c v x- b bo- 3 . J = f r . * = b : = #rau,r + J; ebt X *b3+ fr Jr r\P * T = * (szu'*+C

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G"'\'o'J= X . , : q r , 1".= q" -X !o. = L't c<,\a\iv e t", to. 't.: { o ' t g t t : - \ ' \ 5 : 3 , J t ' j 3 | , t o " ftz' A ' 3 - KO ' "rL : j , 3 6 i " 57.6;" E, Xc;4, : eft (-r,r iYsa ( q)(3a t )* (q) ( sT,u)* (.Xr'1,,{) xc -- \ . = to *x l r " : z14. 3 \'^.ti T *\ - *tr _ i r - - t . \ L'J. T;, +:E*, -Fr3 : G tl),- g t+€ tt), r * C,#..:)' * h ('f(.,b)r - t (a)(q,*)' i",{ 6A (. ,,")' r)+ (s,z\(57:,u) r (, ,)(ll) = l,{8}i n 8o \$,, +^,=ts 5.nr ;ar--{^an*- a"-d to tt.^J \-t c.&*q.6k4 =b. /, { \ -r. \ / -\ r,iXru)= + (ao,*Xq)' + S (r u)/rz)' - *(*"X a')' c - = l K b b , B ' ' , a t (t )[+,:a)'* (,,vr+)i T- 4.8 in, PROBLEM 9.47
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