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How can we find the direction of acceleration in pulley systems so that we can write equation of motion for different parts of the pulley system. Do we have to assume acceleration in some particular direction?

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    $\begingroup$ You may just assume the acceleration to be x in a particular direction. If x comes out to be -ve, you know that it was in the opposite direction. $\endgroup$ – Sam Oct 2 '19 at 9:07
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Yes, it depends upon the force, that resultant force acts in which direction like, take this example If pulley is hanging from a rigid support say roof and masses are connected as shown in figure given below. (assumption: block m2 is heavy then M)
enter image description here

Fbd becomes enter image description here now as you seen in diagram, how the resultant force shows the direction of acceleration of body.

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  • $\begingroup$ Isn't there a more suitable way to find out direction rather than looking at figure and figuring out direction of acceleration? $\endgroup$ – user12076043 Oct 2 '19 at 9:03
  • $\begingroup$ Logic behind the direction is force, it depends upon you, how fast you analyze the situation, which block should go down and which should go up. $\endgroup$ – Yuvraj Singh... Oct 2 '19 at 9:08
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You choose a direction of positive acceleration and work with this direction consistently.

If the acceleration turns out to be negative then you know it is in the opposite direction to direction you chose.

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