Problem 2.9

This is the following question.

[![This is how i tried, but I know it is wrong.][2]][2]

This is our attempt but We can't seem to solve it with inertia.

New attempt according to your approach

  • 1
    $\begingroup$ Can you edit out the contact information for a seemingly random person that is appearing in the bottom of the image? $\endgroup$
    – hazzey
    May 22, 2017 at 14:20
  • $\begingroup$ Done. It's not there anymore. $\endgroup$
    – Shahryar
    May 22, 2017 at 22:02

1 Answer 1


The first step in a problem like this is to draw the relevant free body diagrams. You sort of did this in the top left diagram, but not really. What you want to do is to split each mass and inertia up into a separate free-body diagram. i.e. one FBD for mass 1, one FBD for pulley 1, one FBD for mass 2, one FBD for pulley 2. Then, for each FBD, write down the equations of motion: $\sum F = m a$, $\sum M = \Theta \alpha$. That would get you 8 equations (although 2 will be trivial as the 2 masses have no applied torque and no rotations, so the equation will be just 0=0)

The diagram you drew, with everything all together, is going to get you confused. For example, your second equation looks like $\sum F = T_1 - m_1 g +T_2 + T_3=0$. That's probably wrong, because $T_3$ does not act upon the 1st mass. If you draw out separate diagrams it will be easier to set up the correct equations.

Once the diagrams and drawn and you have the correct 8 equations, solving the equations is straightforward.

  • $\begingroup$ For some reason no student i have ever seen bothers to draw the freebody diagrams on separate drawings. But for some other reason everybody who regularily does this kind of stuff almost always seem to do so. And i must admit that as a student i didnt either. $\endgroup$
    – joojaa
    May 22, 2017 at 15:29
  • $\begingroup$ @Daniel I followed your approach can you please confirm it if it's right or not. or if there is something missing or not? I've edited the solution above. $\endgroup$
    – Shahryar
    May 25, 2017 at 17:18
  • $\begingroup$ This is much better... The question is hard to follow with the original picture edited out, so I'd suggest to put that back in. Then, I'm not sure that I understand equation 1... it's hard to read the handwriting. It looks to me like the right hand side is theta_p a / sigma^2 ? If so, then what is sigma? or is that supposed to be a "r" (for radius)? $\endgroup$
    – Daniel K
    May 30, 2017 at 1:50

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