The moment of inertia I of an object is a measure of how easy it is to rotate the object about some fixed point. In engineering mechanics, it is sometimes necessary to compute moments of inertia with respect to a set of rotated axes. These moments are given by the equations.

Use Product-to-Sum Formulas to show that

and

Transcribed Image Text:

I, = I, cos 0 + I, sin² 0 – 21y sin 0 cos 0 I, sin? 0 + I, cos² 0 + 2Ixy sin 0 cos 0 I, + I, I, - I, cos(28) – Ixy sin(20) 2.