How do mass affect the acceleration of a pulley?

Hi, i am doing physics 20 and i am still quite new at this stuff. I have a base understanding of how the mass affect the acceleration but i can’t find a way to explanation of why the the mass affects the acceleration by making it faster or slower of a pulley for my lab like this one http://ift.tt/1isuDUJ

And i believe newton 2nd law has to do something as well but i dont understand it if there’s no force applied how acceleration could be found? If anyone could help me with this thanks!

http://ift.tt/1isuDUL

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