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"One end of a rod of uniform density is attached to the ceiling in such a way that the rod can swing about freely with no resistance. The other end of the rod is held still so that it touches the ceiling as well. Then the second end is released. If the length of the rod is $l$ metres and gravitational acceleration is g ms−2, how fast is the unattached end of the rod moving when the rod is first vertical?"

Tangential Velocity of a Rotating Rod

This question has been asked before and answered using moment of inertia and GPE. My question is when deriving the answer, it seems as if the GPE of each infinitesimal element is not directly converted into RKE but the whole system's GPE is converted into RKE. Would this be down to some conservative forces between infinitesimal elements in the rod that affect the energy of each element but such that the overall energy of the rod is conserved? I can't seem to wrap my head around the fact that conservation of energy is not held on each infinitesimal strip of mass rho*dx.

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Yes, there are internal forces that hold the rod together. If there were no internal forces (imagine if the rod suddenly turned into sand), every piece of the rod would simply fall straight down.

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  • $\begingroup$ Is this why it would be impractical to consider the forces/energy on that infinitesimal strip as we do not know them all but we do know the relevant forces on the extended body? $\endgroup$ May 9, 2022 at 7:37
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    $\begingroup$ @DanielWilliamsRuiz It is possible to calculate the internal forces, but if we treat the extended body as rigid, it simplifies things greatly $\endgroup$
    – DanDan0101
    May 9, 2022 at 19:26

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