S3E39. A bead sliding off of a massless rod that rotates with a decreasing angular velocity

In this episode we solve a sister problem of the physics problem S2P2 which we solved in detail in S3E54 while studying how the "Mathematical Equivalence" problem-solving approach works. In particular, recall that in the problem S2P2 we were told that even after the massive bead begins its translational motion along the rotating rod, the system rod-bead still rotates at one and the same, constant, angular velocity. Which means that into such a system an external energy is supplied in order to maintain the said constant angular velocity. Back in S2E54, in which we solved the problem S2P2, we mentioned that fact and said that later on we will investigate the case when there is NO external input of energy into the rotating system and, consequently, when the system is left to its own devices then it will rotate with a decreasing angular velocity. Well, this is the place and this is the time when we address this particular case. Surprisingly, though, the integrals that pop out of the woodwork in this scenario are more than merciful and the overall solution comes out to be quite digestible. As usual, we recommend that our viewers try to solve this problem on their own first, before watching our presentation.