Question

The moment of inertia of a disc about an axis through its edge and perpendicular to its plane is 2400kg meter square.find the moment of inertia of disc about its diameter​

Answer 1

We assume the moment of inertia of the disc about an axis perpendicular to it and through its centre to be known; it is MR

2

/2, where M is the mass of the disc and R is its radius.

The disc can be considered to be a planar body. Hence the theorem of perpedicular axes is applicable to it. As shown in Fig., we take three concurrent axes through the centre of the disc, O as the x,y,z axes ;x and y-axes lie in the plane of the disc and z is perpendicular to it. By the theorem of perpendicular axes,

I

z

=I

x

+I

y

Now, x and y axes are along two diameters of the disc, and by symmetry the moment of inertia of the disc is the same about any diameter. Hence

I

x

=I

y

and I

z

=2I

x

But I

z

=MR

2

/2

So finally, I

x

=I

z

/2=MR

2

/4

Thus the moment of inertia of a disc about any of its diameter is MR

2

/4.