Question

6. Gear A rotates with an angular velocity of 0,= 20 rad/s, where , 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

Given that, tingular velocity (wa) = 2012 Of A Podius of gear w) 520 mm (Vc) = 25 mm (VB): 50 mm (d): 100 mm Abo, OA = 200d. Angular velocity of A le (WA) = 20 : 263) = 8 vad/ WA : 8 radl. ü) A Angular acceleration Of A pe da - dWA dt = 2(0), 40. let de 40A. WA = 4x248 da = 64 vad/s (rii) since NAWAE NB WB R 20 (8) = 50(WB) WB = 3.2 rado

(W) since B and C ove on same shaft. (VIIsince feau CG DONG in perh (iv) since VARA = 8Bag (20) (su) - 50(48) AB= 25.6 rad/ rod/ + So, WR = Wc ei Wc = 3.2 rad (vi) Abo B and c Gears have some angular acceleation since then are located on shame Shaft ie *B=&c =de = 25.6 rad/s Werewo (25)*(3-2) (100). WD (WD = Os radly (viii) A60 re&e=NDO (25) (13-6)-(100) Ko cilka Xoa 6.4 rod (5

Summary Angular (1) Trim Augulas reloity of A (WA) = 8 rad/ acceleration of H ( ) = 64 rad (ei) An Angular Velocity at B (ws) = 3.2 rado = 3.2 radi Ciw) Angulou acceleration of B (g) : 25.6 rad/s (1) Angula velocity of C (we) vil Angular acceleration of C (x) = 256 yod // Nii) Angular velocity of D (WD) = of rad i (vii) Augulat acceleration at D (p) = 6-4 rall; Thank You V
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