Question

dear friend
explain the theorem of perpendicular axes in rotational motion ​

Answer 1

your answer

it states that the moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal to the sum of its moment of inertia about two perpendicular axes concurrent with perpendicular axis and lying in the plane of the body.

eg. moment of inertia of a disc about an axis through its centre of mass and perpendicular to its plane is

Izz=1/2MR2

now,

if I d = moment of inertia of disc about one of its diameter ( along yy or along xx-axis)

by perpendicular axes theorem, Izz=Ixx+Iyy

also, Ixx=Iyy, as mass distribution is identical in both cases,

so, Izz=2Ixx=2I d

I d = Izz/2=1/2(1/2MR2)=1/4MR2

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