Question

2. Determine ly and ky. Hint: Section 1 is the left triangle. Section 2 is the right rectangle. Section 3 is the semicircle and section 4 is the empty circle. (20 pts) у 4 mm mm 4 mm 1 8 mm X -12mm- 16 mm

Answer 1

Area moment of Inesta about Yaxis rodus of gyrofon about you ky Ty D 4mm c we divide the total oved into four parts sm10 co-edragene ABC rectange BCDEF Somirde . De 1 16 mm empty arou moment of onetice of Ale about & axis is Toy = 2 bh² (8) C12-4) loy = 1024 mmt lori moment of chestia abocet centrald Sunday 20 Dy'- boobn3 36 8(12-4)3 36 = 1024 a Reo mi abocet y acab Toy' + A-d² + b 2. (2 1024 + £ 8 (12-4) (3 (12+)} 1024 q = 1024 Oy 1024 mmk > MI of redangl obout to Centro de t@g' I bh? (8+4) (@x4) Toy - 512 mm 12

MI o rectangle about y och og & A. d² + (x4) (3+4). (12) ² STO Iay IOy 14 336 mm po MIG Semi cirde about Its Centroid Paralel to yosun is I y tra (454 32T mmt MI of semicirde about y axis IOy - TOY + Adz 327 + TrºC2)^ = 327 + T (4²) (12) oy 1184 TT Iy - 3719.6457 mmt mmt paralls to your MI of arde about it (entroid T2 - 4T y as MI of corde about Ig I0y + Ad² - 4-t + T r²d² = 4tt + T 2² 12² - 580 TT 1822. 1237 mmt mmt Joy

moment of @ Ineta Iy about y ax's in I oy + l@g+ ioy - IOy Ty = 1024 Ty = lengdoseas + 14336 + 3719.6457 - 1922-1237 reco2o8615BO OD 17257.522 mmt L A A= A + A + A3 - A 12bh + b-h + r - TP² = 1.888 + 12x8 + T 4² T.22 Q - 32 & 96 + 8T - 4T A 140.5663 mm2 ky 17257522 140.5663 ky 11.0802 mm