Question

6. Gear A rotates with an angular velocity of 04 = 20rad/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 = 2 rad , Find: i) ii) iii) iv) The angular velocity of gear A The angular acceleration of gear A 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

Angular acceleration of gear A will be find out by differentiating angular velocity .

Given data :- hear rotates with angular relocity WA = 2002 rad's Radius of Gear A= 20 mm B = 50 mm 1) ! C - 25 mm 100 mm. when A 2 rad. (i) Angular relocity of hear A. 2x (2 7² WA= 2012 WA = 8 rad/s

(is Angular acceleration of hear A :- dw dol dt w.dw. dw dt do LA do LA = 200.d (2017 2012 - 400 do 3 80A = 2 rad .. KA= 64 rad/s2 (113) Angular velocity of Gear By law of chearing & BO- NA WA = ro.We . 8x20 3.2 rad/s. WB² hear B. Angular Acceleration of By of learning :- LAVA = Lg. & B. law 64 X20 i do = 25.6 rad /8². ♡ Angular relocity of year ci- Geen B & near G same Shaft .. Angular velocity & Acceleration of hear a will be same Gear B. We = 3.2 rad/ w Anguiar acceleration = de = 25.6 rad/s².

h) Angular velocity of hear Die law of hearing. By doi Wo. do. we 25% 3.2 0.8 rad/s. 100 Angular Acceleration of Gear D:- By law of heariny. hearity. donc doing a Le do 258 25.6 Yo = = 6.4 100 rad/32.