Answer to Question #197100 in Physics for Dua

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