Question

6. Gear A rotates with an angular velocity of 0,= 20 rad/s, where 0, is the angular displacement of gear A, measured in radians. Gears A, B, C, and D have radii of 20 mm, 50 mm, 25 mm, and 100 mm, respectively. When e = 2 rad , Find: i) The angular velocity of gear A 11) The angular acceleration of gear A 111) The angular velocity of gear B iv) The angular acceleration of gear B The angular velocity of gear C vi) The angular acceleration of gear C vii) The angular velocity of gear D viil) The angular acceleration of gear D (30 points)

Answer 1

solution: Geiven: Was 2 OẢ, TA = 20mm, rg = somm, rc = 25 mm, roz 100mm, O A = 2 rad Augular relocity of gear A,WA= 20$ 212² :.WA= 8 radis Ansci) For motion of gear A, CA dOA WA WA = 20$ d (288) 2 - 20 A 2dBA . CA dBA - 4 BAP LOA 4 (21² 2 .:KA = 40 XA 16 rad/s2 Ans (ii) B crear A is in mesh with gear LB LB = CARA :LB LA RA MB = 16 (30) 20 50 XB = 6-4 radls2 Am (iv)

WBIB = WARA i'. :: W1BE WA (1) 8x6 WB = 88 (30) "WB = 3.2 rad's An (iii) Gear B and c are attached together . Wc = WB Wc = 3.2 radis Ans (v) and dc=2B Xc = 6.4 rad /s² Aus (vi) C Gear Dis in mesh with gear :: WD R = Wc rc wb: wc le ) = 3.2 (25) : WD=0.8 radis Ans (vii) and acrc Xoro :: LD: 2c Gheo ) = 6.4* hx (200) XD = 1.6 rad) s² Ams (viii)