Principle Axes and Euler's Equation

1. May 2, 2004

Ed Quanta

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. May 3, 2004

kuengb

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.

Bruno

3. May 4, 2004

kuengb

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>