Question

If moment of inertia of uniform disc about any diameter is (mr^2)/4 , its moment of inertia about tangent parellel to the diameter is

Answer 1

I=I(dimeter moment of inertia) +I(tengent ka moment of inertia) kar do ho jayga

Answer 2

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

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

2

/4.