Q7.26 (a)     Prove the theorem of perpendicular axes. (Hint: Square of the distance of a point (x,y)  in the x-y     plane from an axis through the origin and perpendicular to  the plane is x^{2}+y^{2}).

Answers (1)

Consider the figure given below:  

                                       Rotational motion,    20190

The moment of inertia about the x-axis is given by :

                                                   I_x\ =\ mx^2

And the moment of inertia about the y-axis is :

                                                   I_y\ =\ my^2

Now about z-axis : 

                                        I_z\ =\ m\left ( \sqrt{\left ( x^2\ +\ y^2 \right )} \right )^2

or                                    I_z\ =\ I_x\ +\ I_y