How Do You Label Forces in Multi-Body Systems?

[Miike012]

I know how to create the force diagram but when the system is created of two or more bodies in motion I don't know how to properly create the formulas.

For instance look at the diagram I made of two bodies moving..

1. Ʃ (torque) = T1(R) - T2(R) = (I)(a/R) = (MR^2/2)(a/R) = M*a*R/2

2. Ʃ(F1) = T1 - w1 = (m1)(a)

3. Ʃ(F2) = w2 - T2 = (m2)(a)

With the upward and downward acceleration I am confused how to create my formulas...

 

[grzz]

the equation for the moment (torque) is correct.

Since the mass m2 is accelerating upwards one uses F = Ma in the upwards direction
i.e. T2 - W2 = m2a

and mass m1 is accelerating downwards one uses F = ma in the downwards direction
i.e. W1 - T1 = m1a.

 

[Miike012]

This was my thought process... imagining a free falling body accelerating downward, its weight vector points down... that's why I don't understand if body one is accelerating downward why is w1 positive??

 

[grzz]

re F = ma for body 1

we have W1 - T1 = m1a.

m1 is accelerating downwards and so we have to find the resultant (net) force F downwards.

i.e. we have to find which forces 'help' it to accelerate ...like W1 and so W1 is positive showing that W1 is 'helping' m1 to accelerate and which forces do not 'help' this acceleration ... like T1 and so T1 is negative.