The load L is lowered by the two pulleys which are fastened

The load L is lowered by the two pulleys which are fastened together and rotate as a single unit. For the instant represented, drum A has a counterclockwise angular velocity of 6.0 rad/sec, which is decreasing by 3.0 rad/sec each second. Simultaneously, drum B has a clockwise angular velocity of 4.0 rad/sec, which is increasing by 5.2 rad/sec each second. Calculate the accelerations of points C and D and the load L.

Solution

Solution:

For acceleration in y direction we can directly find using angular acceleration as same radial acceleration will act in y-direction at point C & D.

acceleration for A= angular accleration/radius of drum

   = -3/(5/12)

   = -7.2 ft/s2

this will act in y-direction at C

similarly

acceleration

acceleration for B= angular accleration/radius of drum

= 5.2/(5/12)

= 12.48 ft/s2

this acceleration will act at point D in y- direction

as we can use direction of both accleration are in different direction, therefore resultant of these two will act at load L

acceleration at L = 12.48-7.2

=5.28 ft/s2