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**problem:**

three equal masses connected by light rods, the masses are positioned at (a,0,0), (0,a,2a) and (0,2a, a) now i work out all the products, and moments of inertia to get the inertia tensor, the thing that is baffling me is how you can have Ixx = 10ma^2, with all off diagonal products of x (Ixy, Ixz,) equal to zero. this clearly shows that one of the principal axes is the x - axis, but i dont see how this can be the case when the centre of mass clearly doesnt lie on the x axis(im picturing a triangle with a point on the x axis, and its base in the zy plane). unless this result simply means one of the principle axis is parrallel to the x axis?

its just kinda weird

help?

three equal masses connected by light rods, the masses are positioned at (a,0,0), (0,a,2a) and (0,2a, a) now i work out all the products, and moments of inertia to get the inertia tensor, the thing that is baffling me is how you can have Ixx = 10ma^2, with all off diagonal products of x (Ixy, Ixz,) equal to zero. this clearly shows that one of the principal axes is the x - axis, but i dont see how this can be the case when the centre of mass clearly doesnt lie on the x axis(im picturing a triangle with a point on the x axis, and its base in the zy plane). unless this result simply means one of the principle axis is parrallel to the x axis?

its just kinda weird

help?

**i actually get the right answers, and i understand that for the rest of the tensor (Iyy, Izz, Iyz) its a diagonalisation problem to find the other principle axes for this shape/orientation. its just i have issue with the physical meaning of what going on here with the x axis.**

cheers