5. Consider a thin homogeneous plate with principal momenta of inertiaalong the principal axis x1along the principal axis x2II,> I,I3=I;+I¡ along the principal axis x3Let the origins of the x; and x; systems coincide and be located at the center ofmass 0 of the plate. At time =0, the plate is set rotating in a force-free mannerwith an angular velocity 2 about an axis inclined at an angle a from the plane ofthe plate and perpendicular to the x-axis. If I,/I, = cos 2a, show that at time t%3Dthe angular velocity about the x-axis isw, (1) = N cos a · tanh(2t sin a)

Given, Consider a thin homogeneous plate with the principle moments of inertia, I1 along the…

5. Consider a thin homogeneous plate with principal momenta of inertia along the principal axis x, along the principal axis x2 I I > I I;=I;+I¡ along the principal axis x3 Let the origins of the x; and x; systems coincide and be located at the center of mass 0 of the plate. At time t=0, the plate is set rotating in a force-free manner with an angular velocity 2 about an axis inclined at an angle a from the plane of the plate and perpendicular to the x-axis. If I,/I, = cos 2a, show that at time t the angular velocity about the x-axis is w,(1) = 2 cos a · tanh(2t sin a) %3D

5. Consider a thin homogeneous plate with principal momenta of inertia along the principal axis x, along the principal axis x2 I I > I I;=I;+I¡ along the principal axis x3 Let the origins of the x; and x; systems coincide and be located at the center of mass 0 of the plate. At time t=0, the plate is set rotating in a force-free manner with an angular velocity 2 about an axis inclined at an angle a from the plane of the plate and perpendicular to the x-axis. If I,/I, = cos 2a, show that at time t the angular velocity about the x-axis is w,(1) = 2 cos a · tanh(2t sin a) %3D

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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