1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

When does the bead fly off the rod?

  1. Aug 25, 2015 #1
    1. The problem statement, all variables and given/known data
    A rod of length L is fixed at one end, and rotates in the X-Y plane with angular velocity ω. (To be clear, it is sweeping out an area of ##π (L/2)^{2}##.) A bead starts at position ##r(0)=L/2## with ##\dot{r}(0)=0##. Find ##r(t)## and the time it takes for the bead to fly off the end of the rod.

    2. Relevant equations
    ##F=ma##


    3. The attempt at a solution
    First, I wanted to find an expression for the velocity of the bead in general:
    ##v(t)=\dot{r}\hat{r}+rω\hat{φ}##

    Then I find the acceleration of such a situation:
    ##a(t)=(\ddot{r}-ω^{2}r)\hat{r}+(2ω\dot{r})\hat{φ}##

    Then I need to apply the 2nd law and solve the diff eq. My question at this point is: Is this problem readily solvable in this coordinate system, or do I need to switch to something else like ##r(φ)## first?

    I've played with a few attempts, and my best guess right now is:
    ##\dot{r}(t)=(L/2)e^{(ω/m)t}##
    or
    ##\dot{r}(t)=(L/2)e^{(2ω/m)t}##

    (and of course the position is just the integral of that)

    But I'm not really confident on that answer...
     
  2. jcsd
  3. Aug 25, 2015 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    OK

    Using polar coordinates is good. No, you do not need to express r as a function of angle.

    This solution does not satisfy ##\dot{r}(0)=0##. Also, the argument of the exponential should be dimensionless.

    Can you state the differential equation that you need to solve?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: When does the bead fly off the rod?
  1. Bead on rotating rod (Replies: 3)

  2. Bead on a rotating rod (Replies: 16)

Loading...