Question

6. Gear A rotates with an angular velocity of 0A = 20 rad/s, where e, 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) ii) The angular velocity of gear A The angular acceleration of gear A DA The angular velocity of gear B The angular acceleration of gear B The angular velocity of gear C The angular acceleration of gear C The angular velocity of gear D The angular acceleration of gear D vi) vii) viii) (30 points)

Answer 1

Q1 Civen Data [WA 2 2o radi sec - (1) NA 20mm MB = 50mm orc= 25mm ro 100 mm when for = grad , Salution 10) Angular velocity of gear a Simply put value of OA in eq, lll WA 2 x (21? ] (P rad) sec = And Angular acceleration of goar A x = dw dwa (2x2) (06) I don dt 11 dt

doa angular acceleration of aby dt definition [olat 4 (O.)(wal ] Pust values of above equations LA 4 x 2 x 8 pela 64 mod sm2 Ans ران Angular velouty of _gear B (WB) لیا We know that Crear in meshing fallo Velocity at pains of (velocity at pand of Contact Contact B V= A AWA V8 918 WB If A WA = MB WB WB2 NA MB WA

WB 20 :) (2014) 50 WB = (5) 100%)] put value of LOA = 2 (wg = 5x1274 10 16 5 3.2 rad I see = Ang ling Angelar acceleration of B (08) 08 de B dt 5 (201) (dBA dt (*)(2 (206) (WA) XB 8 x 2x(2) x 18) 6484 5 51.2 rad 1 sec?

lv) Angular reloudy of gear C (wed Now look in to figure of given question, wise that Shaft of с gen Bf gear is samy Hena they will ratate with same speed (wpis we) wc= 1001? 5 (wc و لا 3.2 radIsee) Ars vil angular lar acceleration of gear (de) de = d wc «В → (WB cwc) dt

Angular velocity of gear D Similar case of me mething rule o wyz (916) (wc WD formas y love) 90 WD مهمل) 4 0400) pas = ) >) put the value of OA z 2 (ws 4 S 0.8 rad I sec ) (vii) Angular acceleration of gear & (&D) Lo dwo ) OA) / doa dt det

مه ۱۱ حد( ( و (64) وه را 2 5 x 2x (۰) [ = 6.4 rad/ ser? Ans