1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Finding the potential energy

  1. Aug 1, 2008 #1
    1. We have a cylinder of Mass M rotating about its axis. String is wound around it. Other end is connected to a spring. A mass m is attached to the spring.

    The problem is to find the Lagrangian. My only issue is with finding the potential energy. The problem asks to use the distance of the mass m from center of axis of cylinder to be 'y' and length of spring to be 's'.

    If I take downward positive, I can write,( with U=0 at axis of cylinder) I can write,

    U=mgy + 1/2ks^2

    But if I take downward negative, U= -mgy+1/2 k s^2

    So using two coordinate systems will result in two different end answers for equations of motion.

    Any thing wrong in what I am doing
  2. jcsd
  3. Aug 1, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Re: Lagrangian

    This is just a sign convention and it should not matter in the final answer.
    In this case I think that y and s are independent, right? So the equation of motion for y is just m g y'' = 0 in one convention and -m g y'' = 0 in the other, so it doesn't matter. When you are careful with the sign in imposing the boundary conditions, you should be fine.
    Also, note that flipping the sign on y also flips the sign on s (so you get a different U, but that's ok - but differentiating you will lose the s^2).

    So, to summarize, I don't think there is a problem. If you think there is, maybe you can post some details/
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook