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Say I have a double Atwood machine. A 12kg mass hangs from one side of the first pulley and a second pulley hangs to the other side. This pulley has two masses hanging from it. They are 8kg and 4kg respectively. I originally approached this problem by considering the 8kg and 4kg masses as a single mass relative to the 12kg mass. This lead me to conclude that the system would be in static equilibrium. However the solution in my book involves treating each body separately and deduces that the whole system accelerates relative to the ground. I do not know a lot of physics (did not complete high school). Is this net acceleration as result of torque?

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No!

enter image description here

As we observe from the figure. The lower pulley has $4kg$ and $8kg$ masses hanging on either side. Since the masses are not equal. The masses will have acceleration and thus the lower pulley has acceleration which accelerates the mass $12kg$.

enter image description here

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    $\begingroup$ What did you use to draw these? They're beautiful! $\endgroup$ Commented Dec 28, 2016 at 9:37
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    $\begingroup$ Corel draw @probably_someone $\endgroup$ Commented Dec 28, 2016 at 9:40
  • $\begingroup$ @DeepakSuwalka "The masses will have acceleration and thus the lower pulley has acceleration which accelerates the mass 12kg." How does that work intuitively? The blocks are the ones with acceleration, not the lower pulley. $\endgroup$
    – Jon
    Commented Mar 16, 2021 at 22:57

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