Question

Please Help! Will thumbs up

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 , = 2 rad , Find: i) The angular velocity of gear A ii) The angular acceleration of gear A iii) The angular velocity of gear B iv) The angular acceleration of gear B v) 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)

Answer 1

irven angular velocity of A, WA= 281² rad sec gear A, QA = zrad NA 20 mm ro = 50 mm rc= 25 mm こ rd Dommi 2 sec at CA= doa is angular velocity of year ear A 2 WA = 2(2)*= 8 gad ii> angular accel" of gear Az daawa d (20A?) = 2x2 dt =4WA DA XOA dt = 4x8X2 = 64 rad iii > point contact so velocite at constant is same. VA=8AWA VB = 8BWB but know VA = Ve see? we NA WA = 8B WB 20 X8 = 5° WB WB= 16 5 rad sec (WB) เง) LB z angular acceleration WB=JAWA IOA? 20 x20A² 48x20A. WA A f/2 ro B n 50 4 on? = bax 9xg - lase pool 2

с. us 128 at rad See² 5 viis LD = angulowy accla For gear B, c We coustant same shaft angular veloute of C = 16 rada so an vis angular acceleration of gear Lcz dwe angular velocite of D C D are point contact so WD = Vino XD= d (wo) dt rowc=rowo d (OA? (SAP) at log = £X20AWA OA? V= constant at contact Xc WK = rowo 28 x 16 4 100 5 4 rad Sec Wozas uit Ś x2x2x8 Il !! 32 rad 5 Sec