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!

Can someone check my Lagrangian ?

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Write down the Lagrangian for a cylinder mass m, radius R an moment of inertia I, that rolls without slipping straight down an inclined plane which is at an angle a from the horizontal. Use as your generalized coordinate the cylinder's distance x measure down the plane from its starting point. Write down the Lagrange equation and solve it for the cylinder's acceleration.

    3. The attempt at a solution
    I tried to find the Lagrangian, this is what i have so far, is it right?
    i said that T=1/2mv2+1/2Iw2
    and U= -mgxsina so my Lagrangian would be
    I think this is correct, but I'm not positive. If it is right then should i write I and w (omega) differently? and then continue with the partial differentiation?
  2. jcsd
  3. Dec 7, 2008 #2
    Everything is correct, except that you must express all the dynamical variables (v, w) in terms of x and its derivatives, as the problem tells you. Also you can explicitly specify the value for I, since you know the shape of the body.
  4. Dec 7, 2008 #3
    so if i remember right v=x' but i am not sure what I and w are in terms of x and derivatives. doesn't I have something to do with R, the radius?
  5. Dec 7, 2008 #4
    w is the angular velocity, which for non-slipping case is given by

    [tex]\omega = \frac{v}{R} = \frac{\dot{x}}{R}[/tex]

    and I hope you can figure out the moment of inertia I yourself.
  6. Dec 7, 2008 #5
    I= 1/2 m R2?
    Just checking before I go on with the partial derivatives.
  7. Dec 7, 2008 #6
    Yes, for a uniformly filled cylinder.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?