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Principle Axes and Euler's Equation

  1. May 2, 2004 #1
    A flat rectangular plate of Mass M and sides a and 2a rotates with angular velocity w about an axle through two diagonal corners. The bearings supporting the plate are mounted just at the corners. Find the force on each bearing.

    I am not sure how to find force using Euler's equations since they just relate angular velocities and moments of inertia. The answer is supposed to be F=maw^2/10*sqrt5. Anyone know how I use the 3 principle axes to solve this?
  2. jcsd
  3. May 3, 2004 #2
    Yes, you relate angular velocity and moment of inertia, but that's the point! Because now you can find the m. of in. as a function of time, L(t). From that, you compute dL/dt which is equal to the exterior torque produced by the two forces on the bearings.

  4. May 4, 2004 #3
    Sorry, I've made a mess with moments of inertia/angular momentum. Anyway, my answer remains more or less valid: Find the moments of inertia in the system of the three princple axes to get the tensor of inertia Î, then L=Î*omega, and... <look above>
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