Question

State the expression of moment of inertia of uniform disc about:1)an axis of rotation coinciding with its diameter

Answer 1

Answer:

Explanation:

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,

Iz=Ix+ Iy

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

Ix=Iy

and Iz= 2Ix

Iz= MR^2/2

so finally Ix=Iz/2=MR^2/4

Thus the moment of inertia of a disc about any of its diameter is M R^2/4