Both parts use the inertia ellipsoid .

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Rotation, rigid bodies and accelerated frames · Rotation, rigid bodies and accelerated frames

Action and Symmetry, Ch The inertia tensor, principal axes and Euler angles

Problem

Both parts use the inertia ellipsoid

I_1x_1^2+I_2x_2^2+I_3x_3^2=1

. ((a)) A body has principal moments

I_1=I_2=2.0\times10^{-4}\ \mathrm{kg\,m^2}

and

I_3=5.0\times10^{-4}\ \mathrm{kg\,m^2}

. Classify it as a spherical, symmetric or asymmetric top, find the ratio of the ellipsoid's semi-axis along axis 3 to its semi-axis along axis 1, and say whether the ellipsoid is longer or shorter along axis 3 than across it. ((b)) A different body's inertia ellipsoid has two equal semi-axes of

4.0\ \mathrm{kg^{-1/2}\,m^{-1}}

and a third, along its axis of rotational symmetry, of

6.0\ \mathrm{kg^{-1/2}\,m^{-1}}

. Find the body's three principal moments and classify it.

Browse the problem library