- #1
RohansK
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How to calculate (I) when a mass is turned by the shaft but it is not the mas of the shaft iself, instead it is a mass attatched to the shaft or mass to be turned by the shaft.
The confusion I have is that whenever we calculate the Moment Of Inertia for a circular disc of mass M and radius r it is (0.5)(M)(r^2). But this is for a disc of equally distributed mass around the center.
But consider a disc of mass m and raius r as earlier, which is attatched to a shaft, and we have to turn this shaft to rotate the disc.
Now, If the disc has the same mass and the same radius but the mass is ditributed diferently. Say, that the disc is slender from the center to a radius r3 and from there there is a thicker protrusion in the disc where greater proportion of the mass is concentrated, ( from r3 to r4) and then again the disc becomes slender upto the final radius r ( as radius and mass of the disc remain the same)
So how do we now calculate the moment of inertia. Wont it be different in both the cases as the CG changes due to change in radii of mass concentration.
The confusion I have is that whenever we calculate the Moment Of Inertia for a circular disc of mass M and radius r it is (0.5)(M)(r^2). But this is for a disc of equally distributed mass around the center.
But consider a disc of mass m and raius r as earlier, which is attatched to a shaft, and we have to turn this shaft to rotate the disc.
Now, If the disc has the same mass and the same radius but the mass is ditributed diferently. Say, that the disc is slender from the center to a radius r3 and from there there is a thicker protrusion in the disc where greater proportion of the mass is concentrated, ( from r3 to r4) and then again the disc becomes slender upto the final radius r ( as radius and mass of the disc remain the same)
So how do we now calculate the moment of inertia. Wont it be different in both the cases as the CG changes due to change in radii of mass concentration.
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