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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
3 years 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 230 Points
3 years 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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