Question

three uniform rods OA OB and OC are of each unit length and unit mass are relative to the coordinate system OXYZ the coordinates of A B and C are respectively (1,0,0) (0,0,1) and (√3/2,1/2,0) find principal moment of inertia

Answer 1

Find the principal moment of inertia about the axis $OZ$

Moment of inertia of a thin rod of length $a$ and mass $m$ relative to the axis passing through the end of the rod and perpendicular to it $J=\frac{1}{3}ma^2$ . So, we have

$I=I_1+I_2+I_3=\frac{1}{3}ma^2+0+\frac{1}{3}ma^2=\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$ . Answer