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flash
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The moment of inertia of a sphere rotating about the centre is (2/5)mr^2, but what if it has a hollow 'core'?
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flash said:Sorry, I should have been clearer. There is an inner radius involved, so the thickness is not negligable. I know the basic idea of integration to find the moment of inertia, r^2dm, but haven't done much of it.
dextercioby said:A (2-)sphere is hollow to begin with. So your question doesn't make too mush sense.
Daniel.
flash said:Thanks for all the replies. I only know the mass of the outer part of the sphere. Here's what I think I will do: Find the density of the outer part, calculate the moment of inertia of the solid sphere with this density and subtract the moment of inertia of the inner sphere with this density. Will that work?
OlderDan said:Therefore the volume of a sphere is zero. Even mathematicians resort to "common usage" when it serves their purpose. I've never heard anybody say "the volume of the region bounded by a shpere of radius R" is . . . .
We of course are making the same mistake when we talk about the area of a circle. Using its formal definition, it has none.
The moment of inertia of a sphere is a measure of its resistance to rotational motion. It is a property that depends on the mass distribution and the shape of the sphere.
The moment of inertia of a sphere can be calculated using the formula I = 2/5 * mr², where m is the mass of the sphere and r is the radius.
The moment of inertia of a sphere is important because it is used to calculate the rotational kinetic energy of the sphere, as well as its angular acceleration and angular momentum. It also plays a role in determining how the sphere will behave when subjected to external forces.
Yes, the moment of inertia of a sphere does depend on its density. This is because the distribution of mass within the sphere affects its rotational motion.
The moment of inertia of a sphere is the same as that of a point mass located at its center of mass. This means that a sphere has the smallest moment of inertia for a given mass and radius compared to other shapes, making it easier to rotate.