Proving Rotational K.E. Formula?

  1. Dec 2, 2012 #1
    The total kinetic energy (as viewed from one inertial frame) of a free, rigid body is the sum of all the infinitesimal kinetic energies of the components that comprise the body.

    How do we prove that for a rotating body

    [tex]E_k=\frac{1}{2}\left(M_{T} v_{c}^{2} + I_{c} ω^{2}\right)[/tex]
  2. jcsd
  3. Dec 2, 2012 #2
    Where MT stands for the total mass of all the infinitesmal components combined.
  4. Dec 2, 2012 #3


    User Avatar
    2015 Award

    Staff: Mentor

    Integrate ##\int \frac{1}{2}v^2 \rho dV## (in other words, kinetic energy = 1/2m^2 for all infinitesimal m) and split v into components from translation and rotation and you will get the correct result.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Proving Rotational K.E. Formula?
  1. Momentum and K.E. (Replies: 11)