Question

In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:

(a) v = xcosθ + ysinθ

(b) v = xcosθ – ysinθ

(c) v = ycosθ + xsinθ

(d) v = ycosθ – xsinθ

This question was addressed to me during an interview for a job.

My doubt stems from Moments of Inertia for an Area About Inclined Axis topic in division Moments of Inertia of Engineering Mechanics

Answer 1

Right answer is (d) v = ycosθ – xsinθ

Best explanation: In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.