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Let's say a body $a$ applies a force $\vec F_b,_a=\vec F$ as shown in the figure. so according to the third law the body $b$ also applies $\vec F_a,_b = - \vec F$

so the bodies start rotating about their COM with increasing velocities.So mechanical energy is increasing with time but there is no work being done on the system from outside. what am I getting wrong here. Please explain.

John Rennie
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Subhranil Sinha
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    So far your major mistake is to not include a diagram... :-) – CuriousOne Apr 08 '16 at 05:38
  • sorry, I m uploading it – Subhranil Sinha Apr 08 '16 at 05:39
  • done @CuriousOne – Subhranil Sinha Apr 08 '16 at 05:43
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    Why does the energy have to come from the outside? Body A can have an internal energy source. – CuriousOne Apr 08 '16 at 05:50
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    The third law requires the forces to be colinear otherwise angular momentum is not conserved. See Newton third law and collinearity of forces. In fact I think your question is effectively a duplicate of this question, though I won't close your question until you've had a chance to comment. – John Rennie Apr 08 '16 at 06:05
  • @JohnRennie: The OP talks about bodies and not about particles, though, so they can be extended and they can have internal angular momentum. A typical example of where exactly this phenomenon occurs is in the tidal coupling of Earth and Moon. The Earth spins down, the Moon is tidal locked and the lunar orbit increases in size. Indeed, my guess is that if we assume that the size of his bodies in the drawing indicates the size of two Earth sized planets and the orbit is also to scale, the tidal coupling would probably be so strong that it would melt the crust of both. – CuriousOne Apr 08 '16 at 07:05
  • Ok Sir @Rennie you can kindly close this question now – Subhranil Sinha Apr 08 '16 at 07:57

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