# Calculating Moment of Inertia of a Sphere

• Bucky
In summary, the author was confused about what equations to use for finding the inertia of a sphere and was looking for help. He found equations for cylinders and cubeoids and was wondering if this is what inertia is usually measured in. He was also wondering if inertia has anything to do with where on the body a force is applied. Finally, he was wondering how inertia is calculated in XYZ coordinate and if it is necessary to find the inertia along a non-axis-aligned vector.
Bucky
Hi, I'm in the middle of programming an inertia system and am only really just starting to appreciate what the heck inertia is :) I have been taught inertia, but I haven't actually applied it in a real situation (all my exams and tutorials have resulted in formulae giving answers like 2/7Ma^2).

So I've written a function to find inertia of a sphere and I've plugged some numbers in. I'm a bit confused over what formulae to use for starters.

I can sort of see that inertia of the spheres centre might be useless? given that they're totally symetrical? Am I off with this?

For inertia of a sphere about the diamater I'm using the equation 2/5 Ma^2. Is this appropriate?

Also I've plugged in numbers (like I said). I've never got a numerical answer for a system before so I'd appreciate some guidance as to wether or not I'm correct.

sphere at 0,0,0
mass 1

2/5 Ma^2
0.4 * 1 * 4
MI = 1.6 ?

This should be useful: http://hyperphysics.phy-astr.gsu.edu/Hbase/isph.html" .

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sorry to bump an old thread, but I've done some other bits and pieces and have some results that I'd like to ask about.

I took my mass and added a point mass 1kg to it. If m is at the 'point' of inertia the resulting answer is: 1.6kgm sq

if m is at the opposite side of the sphere from the point of inertia the resulting answer is: 17.6kgm sq

firstly should it be this way round? i can't help but think that the bigger number should be for the higher resistance

also, what is the meaning of what i have found? at the end of the day, what do these numbers actually mean?

Ok after reading through another book I've found equations defining inertia of cylinders and cubeoids. These are given as inertia in x, y and z dimensions. Basically...this wasn't what I was expecting. Is a bodies inertia usually provided as a value in X, Y, Z dimensions?

Does inertia have nothing to do with where on the body a force to move it would act?

It has nothing to do with any dimensions. Moment of inertia is calculated with respect to some axis, typically x, y and z.

thanks for the responce!...but i would asume that the width/depth/height are the values that affect its inertia in each axis? for example the inertia of a cube along the x-axis is
$$\frac{1}{12} m ( b^2 + c^2)$$where m = mass, and b and c are the length of the cube along y and z axis.

also, if inertia is calculated through XYZ axis, how is the inertia along a non axis-aligned vector found? interpollation? do you even need to find this? To be honest I've never used inertia in anything (i've just "found" the inertia) so I'm finding it hard to learn.

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## 1. What is the formula for calculating moment of inertia of a sphere?

The formula for calculating moment of inertia of a sphere is 2/5 * m * r^2, where m is the mass of the sphere and r is the radius of the sphere.

## 2. How do you find the mass of a sphere?

The mass of a sphere can be found by multiplying the density of the material by the volume of the sphere, which is 4/3 * pi * r^3. Alternatively, the mass can also be measured directly using a scale.

## 3. Can the moment of inertia of a sphere change?

Yes, the moment of inertia of a sphere can change if the mass or radius of the sphere changes. It can also change if the sphere rotates along a different axis.

## 4. What is the significance of calculating moment of inertia of a sphere?

The moment of inertia of a sphere is an important physical property that helps determine how the sphere will rotate and respond to external forces. It is also used in many engineering and physics calculations, such as calculating the angular acceleration of a sphere.

## 5. Are there any real-world examples where calculating moment of inertia of a sphere is important?

Yes, calculating moment of inertia of a sphere is important in many real-world scenarios, such as designing sports equipment like bowling balls and baseballs, understanding the behavior of planets and other celestial bodies, and in the design of gyroscopes and other rotating devices.

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