Question

10-13 and 10-14 the same diagram

10-13. Determine the moment of inertia about the x axis. 10-14. Determine the moment of inertia about the y axis. x2 + 4y2 = 4 Im 2 m Probs. 10–13/14

Answer 1

Solution : 10-13. Moment of Swertia about savus 18 x²+42² we know we. Know = 1 = IdI = Sadary? now, d A = x I= ''x dy g? we know, x → +4y=4 = 14-44? 80, P- j'su -kig') go dy ļy Juragedy 2 S'Vragedy stan x = yosh dyz tsmodo = y = sint where, o s dy = cost at .O ste /2 80, I = 225" sualt) Ji- siune) coscedt 20 sia't cos'tdt we unow. Colt I + Cos (2)

(papieros - , = 'opl]) ? op ('9,5W) -13 12 'pp (in mo 717 (('94-17,S of »92 11) (1992-1) : fp = 'op 7 € 492 = 'np +2=10 +P(1280) 717 (4760)-1) - - 2 25 M2 - Ceget) It contat & sin't a 1-Ca(2 t) tpornosti) 17"* mice -

ost (10- scat uav,) -15 Cos'o, tcos au to p 7 = a (cuya - ! (+ 1602.0.) don) ru (c)-( + ": tramida)) - † (10]." - Ź ( ["ides + ["carbus du)) - § (103" Į (10.3." + [*cas es du)) Let uz = 20, dvs. = 2do, 180, 100, z do, = (10.1." - (0.), " + * coque du.)) Eg (10,3."- ()" + iv in Ore) ")) to moment of Inertia about x-axis.

10-14 solution: - x²+uy?-u + Lux d A = dx y I - 1 LA x2 = f'y dx x² we knows o B g? + 4y?=4 ay?- art y = 1(4-32J so, I = f oc? 114->?) dy s x? JR4-24y.dy integrating it in the same way as done in previous post Afien so, Iy = "/" I moment of Inertia about y axis.