Theorem of perpendicular axes

Q.  Which of the following relations is used to represent theorem of perpendicular axes?
(H = Vertical axis, I = Moment of inertia and K = Radius of gyration)
- Published on 21 Sep 15

a. IPQ = Ixx + AH2
b. IPQ = Ixx + Ak2
c. Izz = Ixx + Iyy
d. Izz + Ixx + Iyy = 0

ANSWER: Izz = Ixx + Iyy

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    Discussion

  • Sravanthi   -Posted on 24 Nov 15
    - According to theorem of perpendicular axes, the moment of inertia Izz about x-x and y-y is the sum of moment of inertia about x-x axis and y-y axis when Ixx and Iyy are mutually perpendicular to each other.

    The relation between Izz, Ixx and Iyy is given as Izz= Ixx + Iyy

    - According to the theorem of parallel axis, the moment of inertia about any axis is the algebraic sum of moment of inertia about centroidal axis and the product of area of section and square of distance between centroidal and reference axis.

    Iaxis = Ixx + AH2

    here, A is area of rectangle and H is the vertical distance

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