Finding the Minimum Coefficient of Static Friction for a Half Atwood Machine to Slide

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What minimum coefficient of friction do you need to get a half Atwood machine to start moving?

Here are all the other Atwood Machine problems.
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thank you very much for explaining in 5 minutes, what lecturers couldn't in the space of a couple of hours!

merkins
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At 4:51 why is it the minimum Coefficient? Why is it not just equal to? I mean isn't it just about to slide? So that's the maximum friction? So like maximum coefficient?

hajar.h