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I need a little help completing a mechanics problem. If you have a pendulum put vertically up with a rigid rod and ball on top of the rod and you give the ball some initial velocity $v_x$ how would I find how long it would take the ball to hit the bottom of the swing (travel $\theta=180$)? I'm stuck.

Ok so I used energy to get: $$v=\sqrt{\frac{2}{m}(\frac{1}{2}mv_i^2+2mgL)}-2L(\cos\theta+1)$$ I am currently trying to find theta as a function of time so that I can integrate with respect to time.

It just dawned on me that I can't find theta as a function of time because it is a non-linear diff eq. So the only way I will be able to solve this problem is if I approximate (most likely with small angle approx.) which will throw my answer way off.

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closed as off-topic by John Rennie, heather, ACuriousMind, AccidentalFourierTransform, knzhou Aug 10 '16 at 21:47

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – John Rennie, heather, ACuriousMind, AccidentalFourierTransform, knzhou
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Perhaps the work in this answer is helpful? $\endgroup$ – Floris Aug 9 '16 at 3:39
  • $\begingroup$ The question is about a specific physics concept and shows some effort to work through the problem. Closing it is against the rules. $\endgroup$ – user259412 Aug 9 '16 at 21:09
  • $\begingroup$ @peterh: What is the specific physics concept here? The question shows work and is thus better than most homework-like questions we get, but it still just asks how to solve a given exercise. $\endgroup$ – ACuriousMind Aug 10 '16 at 11:00
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Try thinking about some of the following:

1) Conservation of energy and how you can exploit $m*g*h$ to find the bob's velocity. Can you ignore the mass of the rod? That's a critical question.

2) The bob's velocity will always be tangential to the circular curve it's following.

3) Perhaps the relation $dS=R*d\theta$ can help when considering the circular path.

4) Does $dT=\frac{dS}{V}$?

5) Isn't $V$ dependent upon $\theta$ as it increases from $0$ to $180$?

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  • $\begingroup$ Ok I was able to get velocity as a function of the angle using energy. If I can find the angle as a function of time I can get the time it takes by integrating. $\endgroup$ – Shrodinger 2016 Aug 8 '16 at 23:37
  • $\begingroup$ @Shrodinger2016 Try thinking about hints #2, #3, #4, and #5. Keep at it. It's not easy. $\endgroup$ – Inquisitive Aug 8 '16 at 23:42

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