I've learned that the torque on an object is just $ \text{perpendicular force}\times\text{radius}$ and that has worked well for things like seesaws but it doesn't take into account the torque of the object itself!

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In the picture the rod has a total mass of 5kg, and by definition the torque on the right is greater than that on the left. $$T=Fr$$

I am supposed to solve the question

What distance to the left of the fulcrum (triangle supporting the rod) would I have to put a 3kg weight to balance the rod?

I've tried calculating the net torque $T_{net} = I\alpha$ but I don't really know how to approach this. I'm looking for an explanation more than an answer.

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    $\begingroup$ Homework question in disguise. Please note that we do not give answers to homework questions. You need to show your effort. $\endgroup$ – Yashas Jul 22 '17 at 4:26
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    $\begingroup$ First identify the position of the centre of mass of the rod. $\endgroup$ – Farcher Jul 22 '17 at 8:29

Since, this is clearly a homework question and I would suggest trying to research your answer, so I am simply providing some clues at your disposal, I would suggest to read those clues and frame your answer :-

1.) The total length of rod is 60m.

2.) We would practically assume the mass of the rod distributed evenly throughout (i.e. if its mass is x kg, then on one side of the midpoint of rod it will be x/2 kg)

3.) In order to balance the rod,

Torque Produced due to the weight of rod on right side = Torque produced by the 3kg weight as well as the weight of rod on left side

I have provided you all the simplest clues required to solve your homework exercise, I would recommend reading them properly and furthermore not to ask homework questions on this site since, it is more certain to be bombarded with downvotes.

  • $\begingroup$ Thanks for your answer, but please don't answer off-topic questions - it encourages them and makes them more likely to be asked. Again, this isn't to say your answer is bad - it's rather good. $\endgroup$ – heather Jul 22 '17 at 22:42
  • $\begingroup$ sincere apologies for that... $\endgroup$ – Ajinkya Naik Jul 23 '17 at 5:07

Think of the rod as just another load placed at its centre of mass on a balanced rod. Then you have to balance two loads on an already-balanced rod, one on each side of the fulcrum. This enables you to calculate the position of the 2nd load to make the rod balance.

You are looking for a situation in which there is balance, so the angular velocity $\omega$ and angular acceleration $\alpha$ of the rod are both zero. The equation $T_{net}=I\alpha$ then tells you that the net torque on the rod must be zero. You are applying this equation when you use the condition that the resultant torque on the rod must be zero if it balances.

  • $\begingroup$ Thanks for your answer, but please don't answer off-topic questions - it encourages them and makes them more likely to be asked. $\endgroup$ – heather Jul 22 '17 at 22:42
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    $\begingroup$ @heather The question was not judged to be off topic until after I had answered it. $\endgroup$ – sammy gerbil Jul 24 '17 at 10:43
  • $\begingroup$ if you've spent enough time on the site, you should be able to tell when a question will be closed as off-topic. This is clearly a homework question, and it was when it was posted. $\endgroup$ – heather Jul 24 '17 at 15:06

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