Explore BrainMass

Explore BrainMass

    Lagrange of a rolling hoop without slipping

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A hoop of mass M and radius 1? rolls without slipping along a track which has the shape of a circle with radius 4R. It is subject to gravity. It is confined to a plane, so when the no-slip constraint is imposed there is just one degree of freedom.

    Use the angle d as your coordinate. (This angle gives the location of the center of the hoop,
    as measured from the center of the track circle.) Find T, U, L, and the Lagrange equation.
    For small oscillations find the angular frequency of oscillation c..'. (Hint: Think carefully about
    what the no-slip condition says about the rate of rotation of the hoop compared to the rate of
    movement of its center, given by d. Remember you will have two terms in the kinetic energy -
    which you can assume are due to the translational of its center of mass, and the rotation about its center of mass.

    See attached file for full problem description.

    © BrainMass Inc. brainmass.com March 4, 2021, 7:49 pm ad1c9bdddf


    Solution Preview

    Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.

    ------- Diagram -----------------

    Constrain of motion is
    R = 4R
    R α = 4R θ + C

    Where C is the ...

    Solution Summary

    I have shown very detailed step by step solution to this classical mechanics problem using Lagrange mechanics concepts.