A disk of radius 6 in is rigidly attached to a drum of radius 4 in as shown. The

Question

A disk of radius 6 in is rigidly attached to a drum of radius 4 in as shown. The drum rolls without slipping on the surface shown, and a cord is wound around the disk. If at the instant shown end D of the cord has a velocity of 8 in/sec and an acceleration of 30 in/sec^2 , both directed to the right. Determine the accelerations of points A , B and C .

A disk of radius 6 in is rigidly attached to a drum of radius 4 in as shown. The drum rolls without slipping on the surface shown, and a cord is wound around the disk. If at the instant shown end D of the cord has a velocity of 8 in/sec and an acceleration of 30 in/sec^2 , both directed to the right. Determine the accelerations of points A , B and C .

Explanation / Answer

since the drum rolls without slipping, so the acceleration of D towards right = acceleration of point B towards right

let a be the acc of point A.

So at point A there should be no acceleration as there is no slipping.

So, acc at point A = 0

Acceleration at point B = a*6/4 - a = 30

=> a/2 = 30

so a = 60in/sec^2

acc at B = 30 in/sec ^2 = (Acc of D)

and acc at C = 60 in/sec^2 towards up + 30 in/sec^2 towards left

= 60 j - 30i =

= 67.08 in/sec^2

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