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What is the moment of intertia of a disc about one of its diameters?

What is the moment of intertia of a disc about one of its diameters?

Grade:12th pass

2 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
10 months ago
We assume the moment of inertia of the disc about an axis perpendicular to it and through its centre to be known;it isMR2/2, 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 thex,y,zaxes;xandy-axes lie in the plane of the disc andzis perpendicular to it. By the theorem of perpendicular axes,
Iz​=Ix​+Iy​
Now,xandyaxes 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​
andIz​=2Ix​
ButIz​=MR2/2
So finally,Ix​=Iz​/2=MR2/4
Thus the moment of inertia of a disc about any of its diameter isMR2/4.
Vikas Amritiya
askIITians Faculty 158 Points
10 months ago

Dear student

We assume the moment of inertia of the disc about an axis perpendicular to it and through its centre to be known; it is MR2/2, 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
But Iz=MR2/2
So finally, Ix=Iz/2=MR2/4
Thus the moment of inertia of a disc about any of its diameter is MR2/4.

Best wishes

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