Question

1. The 12-ft beam is initially at rest when the 1-ft diameter drums are given angular accelerations of a1 = 0.3 rad/sand az = 0.5 rad/s2 in the directions shown. 1 ft o 1 ft ali 02 4 ft 4 ft 4 ft a. Determine the acceleration vectors of points A and B on the beam С A B b. Calculate the angular acceleration vector of the beam C. Determine the acceleration vector of point C

Answer 1

solution : 22 oje t=t see B' A Luft uft Kuft to see A e Z Given: Drum Radius (8)= Drum Diameter 2 I ft r [r= 0.5 ft] 21 0.3 rad) see? 0.5 rad / see? L y Note: Beam ABC have well as have {(or) Translation as Scanned with CamScanner acceleration in direction as angular acceleration in z direction. well as rotation motion}

oi + (702) j + O Ê [a] Acceleration vector of the point A is : AA AA 744 ปี 0.5X0.3 j Tan 0.15 ) m) see? ] A (67) in y-direction. Acceleration Vector the point B is : AB oi + (822) ŷ to = 822 0.5X0.5 j [ as 0.25 Ĵ my see? (o in y-direction. 163 Beam with respect have Angular acceleration a Point A : to the d 11 (aB - AA) BA (0.25 -0.15) 4 ft e 12 0.025 rad/see? in counter clock wise directing CSScanned with CamScanner

→ Angular Acceleration of the beam is: [a d = 0.025 rad see 2 Ecw] (ory in Z direction. [0] Acceleration of the point a in Vector form: ac ac 1 a A + ACX a 0.15 ſ + 18H4 X 0.025) i 0:35] in y direction - 0.35 Î m) seed ] () in y.direction. fac [ac (or) Ос Scanned with CamScanner