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!

Length of Pendulum with Variables Only

  1. Apr 17, 2014 #1
    1. The problem statement, all variables and given/known data
    A grandfather clock has a pendulum that consists of a thin brass disk of radius r and mass m that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in the figure below. If the pendulum is to have a period T for small oscillations, what must be the rod length L. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)
    Picture: http://www.webassign.net/hrw/15-54.gif


    2. Relevant equations
    T=2*pi*sqrt(I/mgh)
    h=distance from pivot to com, meaning h=L+r
    I=(mr^2)/2+mh^2

    3. The attempt at a solution
    I've tried to isolate L from the equation, but I can't isolate it. This is what I end up with:
    T=2*pi*sqrt[((mr^2)/2+m(L+r)^2)/(mg(L+r))]
    Cancelling m, I get T=2*pi*sqrt[((r^2)/2+(L+r)^2)/(g(L+r))]
    After simplification, I get T=2*pi*sqrt[((r^2)/2+L^2+2Lr+r^2)/(gL+gr)]
    There is no way to isolate L in this equation, I'm stuck.
    I feel like there must be some piece of information I'm just not seeing, because otherwise this problem is impossible to solve.
    Can you tell me what I'm missing here?
     
  2. jcsd
  3. Apr 17, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    This gets a simple quadratic equation if you square it (would be my first step to simplify it) and multiply it with the denominator.
     
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: Length of Pendulum with Variables Only
  1. Length of a Pendulum (Replies: 1)

  2. Length of a pendulum (Replies: 1)

  3. Length of a Pendulum (Replies: 4)

Loading...