Question

#326

In the following exercises, consider a lamina occupying the region R and having the density function p given in the first two groups of Exercises. a. Find the moments of inertia IX, Iy, and I, about the x-axis, y-axis, and origin, respectively. b. Find the radii of gyration with respect to the x-axis, y-axis, and origin, respectively.

ignore 325, only need 326

Answer 1

-2- 3 2 9-1 2 = 0 4 2 = -1/3 1, 2 | 3* Р(1 , 9)dA R 1-443 Si g (exty) dady 3-8 % ГЈ (32*+43 Јах да у чуму, - зву » І. Т (3*(3-2)* + + (3-5)* - у - у г'I ° +3* - 6 + 4 (3-5)* - 55* ) 4 Jody о

(3-4) sys lo + 4 5 20 ays us - Gye + Ś 5 at 6 4 (3) W 5 20 tot 1 (3) 3 3 + 3 - 3 2 - 3 + (3)5 d pl 20 I z 12 Ty SS x ² p(x, y) da R 3-4 ss x² (2x+y) dx dy o y 3-4 ! (2x3 + x²y) dady

3-9 I dy 3رو-3) 9+ (4-3) ( - لا ( 49 ) ا - ا - و إلا و و 3) | | 3 dy | (2) 1 - درة - ا + د رد-3) - 0- 3ر2) 3 ] -10 lo 2. ل lo 15 (2) -10 اما - (3) + 2 - ق(ع) ار و( و 12 12 2546 ۱ Iy ۔ Io Ixt Ty )2 + 25,46 ۱۱ I 3746 (6) Radius of Gyration | I Ko - ا ر ء وا ر ا A Now, S s dady 6 9

s' (3-9-y) dy V 34 -24 14 3y ho 3-1 le w A = 2 12 20 = 2 25.46 Ke Ky Ko 112.13 > 3.56.79 2 137146 √ 18.73 12 4.3278 2