Question

6. Gear A rotates with an angular velocity of 04 = 20rad/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

Solution Angular velocity of gear A WA= 20 rad/s radius of geor VA= 20mm OBS = 50mm rc = 25mm 80- 100 mm Angulor displacement of geor A , On = 2 red i) Angulor velocity of gear A WA= 2XA 2 = 2x2² 8 rad is - เวโร Angular acceleration of gear A (LA) LA = dWA d (2003) 2x20x doa dt dt dt XA=40AXWA doa dt 4x 2 x 8 64 rad/s2 iii) Angulor velocity of geor Bi Wo ( velocity ration) WA 7 WB WAX NA 8x 20 3.2 rad/s B 50

iv) Anguloy acceleration of X= 440 x w geor & C&B) soby ho wib LB= 4x0B&WB B W = 2x02 فيا = ق چ he 2 bangsaab zs OB و فعال WB = OB 3.2 2 = 1.2649 rad LB = 4x1.2649X 3.2 16.1908 rad/s² ** & Angular velocity of gear c Wc فما = فما ( some shaft Wc. = 3.2 rad/s vi) Angular acceleration of gear c Lc de 16.1908 rod/s² vii) Angular velocity of georo Woo

rc Lр Wc ro = وفا د We X rc 3.2 x 25 ro = 0.8 rod/sec 100 of vii) Angular acceleration 44 px WD gear o do مهما * hoo 2 x help 4x X 0.8 do 2.0238 rad /se Summary i 8 rad's i 64 radlsz i) 3.2 rods iv) 16.1908 rad is v 3.2 rad's vi) 16.1908 rad/s² vii) 0.8 rod/sec vill) 2.0238 rad/s2