A particle of mass m slides down the frictionless surface from height h and collides with the uniform vertical rod of length L and mass M. After the collision, mass m sticks to the rod. The rod is free to rotate in a vertical plane about fixed axis through O. Find maximum angular deflection from its initial position.enter image description here


closed as off-topic by dmckee Oct 23 '15 at 15:52

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  • $\begingroup$ Tell us what you have tried so far and what concepts specifically are confusing. $\endgroup$ – tmwilson26 Oct 23 '15 at 15:19
  • $\begingroup$ i have tried to conserve energy.loss in potential energy equal to gain in rotational kinetic energy + gain in potential energy $\endgroup$ – Dev Oct 23 '15 at 15:24
  • $\begingroup$ Thats a good place to start to get the speed of the particle at the bottom. However, when a collision involves two objects sticking together, it is generally considered inelastic, and conservation of energy can't be used. What other conservation laws do you know that you can consider? $\endgroup$ – tmwilson26 Oct 23 '15 at 15:26
  • $\begingroup$ angular momentum of the system just before and after the collision. this will give me w(omega), not deflection. $\endgroup$ – Dev Oct 23 '15 at 15:30
  • $\begingroup$ Okay, I understand where the confusion comes from, I'll write a quick answer to help you (while leaving it up to you to solve the problem) $\endgroup$ – tmwilson26 Oct 23 '15 at 15:37

There is probably a more clever way to do this, but here are some concepts that may help you along the way. If you have a problem in this type of situation, you need to consider all the conservation laws that are at your disposal. You mention in our discussion in the previous comments using conservation of angular momentum and conservation of energy. These are both concepts that you will need to solve this problem.

Conservation of energy can be used to find the speed of the particle, but upon an inelastic collision with the rod, you know that angular momentum will be conserved.

Knowing the angular momentum, you can then recalculate the kinetic energy of the system (by knowing $\omega$ and the moment of inertia, $I$). Now you can use conservation of energy again to calculate the maximum deflection of the rod.


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