Question

6. Gear A rotates with an angular velocity of QA = 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 04 = 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 viii) The angular acceleration of gear D (30 points) SO

Answer 1

1 given data ~ angular Velocity of Geon A WAJ 202 -) diameterie of gears are dA=20mm do = 25 mm dB= 50 mm do= 100 mm when A= 2 rod c Compound gear Ba Angular velocity of gear A WA = 20$ when OA = arad WA = (2) (2) 2 WA = 8 rod/s doo -) - (40) - (dr) (wo). de d- d (208² da .(ما)(ها)

=) angolar acceleration of Sear A LA = (40A) (WA) when OA = 2 grad WA = 8 rad/s LA = (4) (2) (8) KA=6u nod/s2 WB ZA 2) Angular Velocity of Gear B ! > No. of tooth da ZB dB u diameters of gears Wo = (wa) (da O=2 orad's WA de -) WR18) (20 WA = grad's 50 WB = 32 rad's -) Angolan aleelegasion of gear B: Since Gear A & Gear B are in mesh. Tangen Tangen bial acceleration of Gear in] = Flangentia Flangenbia) accelerat of Gear B aa), (ab), " ador T LAMA = XBIB.

-> do (LA) (same -> KB - (Gu) (2010) (GM) (2007.) - 15.6 8100152 XB= 25.6 rad/s2 angular Velocity Of gear C & (Kac) Gear B and i are on same shaft (Compound gear) Wo = WB = 3.2 rad /s Lc = LB = 25.6 rad/s2 Wo & an wo = 30 20 de do. -> W. = (we) dc (3.2) 25 100 Wo= 0.8 grad /s => dcollo Lo oro Lo= (25.6) (25/100) Lo = 6:4 rad/52