What Are the Moments and Products of Inertia for a Rotating Particle?

[gatechphysics]

Homework Statement

A particle of mass m is located at x=2, y=0, z=3.

(a) Find its moments and products of interia relative to the origin.

(b) The particle undergoes pure rotation about the z axis through a small angle α (see the attached figure). Show that its moments and products of interia are unchanged to first order in α if α<<1.

Homework Equations

The Attempt at a Solution

I am not quite sure how to start part (b).

 

[_coyote_]

I have part (a) which I got to beIx = m(y^2+z^2) = m(0 + 9) = 9mIy = m(x^2+z^2) = m(4 + 9) = 13mIz = m(x^2+y^2) = m(4 + 0) = 4mIxy = mxy = m(0) = 0Iyz = mzy = m(0) = 0Izx = mxz = m(-6) = -6m