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: Moment of inertia question

  1. Mar 11, 2010 #1
    The problem statement, all variables and given/known data

    Consider a rigid body with an inertia tensor I =[30, 0, 0; 0, 40, 0; 0, 0, 20] N m s^2 and angular velocity w=10j+10k rad/s. Determine the moment of inertia about an axis parallel to w and find the rotational kinetic energy.

    The attempt at a solution

    I'm not sure if the fact that this is the principal moment of inertia matters. Also, I thought this had something to do with the parallel axis theorem, but neither mass nor any distances are given. Any help would be appreciated.
  2. jcsd
  3. Mar 12, 2010 #2


    User Avatar
    Science Advisor
    Gold Member

    The fact that you have I along the principal axes will simplify the calculations but is not otherwise important.

    Hint: look at how I transforms under coordinate transformation (i.e., rotation).
  4. Mar 12, 2010 #3
    You will want to solve for the scalar form of I in the direction of w. So you will need to convert w to a unit vector and matrix multiply it on both sides of I to get a scalar value:

    [tex]I = \hat{\omega}^T \bar{I} \hat{\omega}[/tex]

    Knowing the scalar form for I and the magnitude of angular velocity you can simply get the rotational kinetic energy.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook