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My current line of reasoning is to use force diagrams and then

Since [itex]\tau[/itex] = RF sin ([itex]\theta[/itex]) =I[itex]\alpha[/itex],

F =((I[itex]\alpha[/itex])/(R sin([itex]\theta)[/itex]))

Since the net force is generally provided by one or more objects allowed to fall

ƩF[itex]_{y}[/itex] (generally equal to m[itex]_{falling object}[/itex]g- F[itex]_{tension}[/itex] )=m[itex]_{total}[/itex]a + ((I [itex]_{1}[/itex] [itex]\alpha[/itex])/ (R[itex]_{1}[/itex] sin ([itex]\theta)[/itex]))

+ ((I [itex]_{2}[/itex] [itex]\alpha[/itex]))/ (R[itex]_{2}[/itex] sin ([itex]\theta[/itex]) ))... and so on for any of the other I[itex]\alpha[/itex] and ma.

I will then generally plug in a/R for [itex]\alpha[/itex]

At this point, I'm generally not sure what to do. Possible ideas are to do a sum of torques equation, or to attempt to solve for Tension in the x direction.

Another thing that confuses me is when to include translational velocity for a rotating object in my equations.

Thanks in advance.