Question

PERPENDICULAR- AXIS THEOREM

Answer 1

Answer:

• This theorem is applicable only to the planar bodies. Bodies which are flat with very less or negligible thickness.

• This theorem states that the moment of inertia of a planar body about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with the perpendicular axis and lying in the plane of the body.

• Iz = Ix + Iy

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Answer 2

Theorem Of Perpendicular axis :—

• MI of s planar lamina about an acid perpendicular to its plane is equal to sum of its moment of Inertia about two perpendicular axis concurrent with perpendicular axis and lying in its plane.
• Iz= I +Iy

Proof:—

Consider a particle of mass m at P(x,y)

MI of body along x- axis Ix= sigma my²......(1)

MI of body along y-scid Iy= sigma mx² ......(2)

= sigma m(x²+y²)

= sigma mx²+ sigma my²

Iz= Iy+Ix

→ Iz = Ix+Iy