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Say a beam, 3m long from end to end, has a pivot placed at its centre of mass, at half its length i.e. 1.5m. Objects with weight 200N each are placed on both ends of the beam. The system is in equilibrium and thus no turning effect.

Now a force of 30N is applied on one of the ends until the beam turns 15deg to the horizontal. When this force is removed, the moments on both sides are balanced. But, the beam turns, until it becomes horizontal?! If resultant moment is zero, how can the object turn?

Is the moment really not zero, or is there some potential energy transferred to the beam which converts when the force is released?

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  • $\begingroup$ Your conclusion about the beam isn't correct, with a well drawn free body diagram you can show that the rod will not move back to being horizontal as there is zero net torque. Have you tried drawing a FBD for this system? $\endgroup$
    – Triatticus
    Commented May 13, 2021 at 19:32

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The other answers are correct in saying that if the pivot is at the centre of mass of the beam, the beam will not return to the horizontal position when released.

You might have assumed it would return because that is the way in which weighing balances operate. However, those balances have a pivot which is placed slightly above the centre of mass, and that is what causes them to return to the horizontal position when they exactly balance.

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  • $\begingroup$ Take my reputation! All of it, because of that second paragraph! Thank YOU! $\endgroup$
    – El Flea
    Commented May 14, 2021 at 9:54
  • $\begingroup$ You are very kind, El Flea! The offer of your reputation is too much, but if you would like to do me a different honour, please have a look at my profile and consider what it says about my books! $\endgroup$
    – Professor Sushing
    Commented May 14, 2021 at 10:19
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it won't return to zero angle. It will remain in balance at 15deg. In fact, if it has any rotational speed when the force is lifted it will continue to lean.

If you work out the math, you will see that the two weights cancel out the torque on the pivot regardless of the tilt angle.

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