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davidvn10
What is, or how do you find, the moment of inertia of a human being whom is male, 5'10", and 165lbs? I'm unsure where to start or which moment equation to use. Any help would be great thanks.
Alej
Hello.

-Are you considering moment if inertia referring to the mass, aren`t you?. If you don`t know what I am talking about, tell me if you want to consider mass in the calcularion, or you don`t smile.gif.

- Moment of inertia depends on the reference system considered, since it has distance to the mass elements involved. And once is set the reference system, moment of inertia depends on (roughly) how are you rotating the body.

-Actually, you have a matrix (tensor) of inertia.

This all seems complex. But depending on the application it can turn quite easy, because you may set an appropiate system of reference, and maybe, discard some values of the matrix, so you won`t have to get each value. So

Why do you need the moment of inertia of a humang being? What do you need to calculate (get)?


You can seehere, to get an idea.

Note that you can choice between model the human being as a set of continuum bodies (like cylinders, and so), or you can consider it as some balls with mass linked by wire (without mass). The first option is complex, the second is simpler. The difference is in the accuracy of what you get.

This explanation was very general, but tell me some more about what you want and I will help you. Conceptually, is not difficult, but it may require some tedious calculations.

Alejandro
davidvn10
Yes I am concerning the moment of inertia refering to mass. I appreciate your response very much.
Alej
Moment of inertia concerns to mass and distance from an origin.

About mass, how to model the human body:

You can see the human body as a continuum distribution of mass-->so you would need the density in each point of the body, and how to express the volume integral (that`s, what are the limits and dV, in other words, you have to describe each part of human body in a mathematical way, for example, to get the volume of a cone, you need to describe it in the limits of integral, and the dV element). Density can be taken as constant, so no problem there. But the integral of the perpendicular distance to power 2 in the volume, can be difficult, and tedious.

Other approach is the discrete one-> in this you consider the human body as a set of balls linked with wire. Only the balls have mass. So you use a sum (see the reference that I gave you in my previous post for formulae) that`s easier to calculate. Is not as accurate as the previous method (continuum), but it can be enough if you place the balls in the right possitions, with the righ mass each one. I`d go for this approach. When trying to figure out how place mass, take in account the constraints that the sum of mass should be equal to total mass, the body should be equilibrated, with the same mass center of continuum body, and maybe you can look for human body ratios (head to body, arms to head, etc. Maybe in tailor shops you can find something), and then supposing a constant density, you can get some proportions of mass. Depending on your calculations, some apparent contradictions may arise, if you forget that the body considered is a set of mass, so keep that in mind.


After the mass, you have to deal with distances. This means that you have to place the coordinate system in a good place. I suggest you to place the system in the mass center, in such a way that axes follow the symmetry axes of the body. In that location, it will be easy get the moments of inertia. After that you can get the moments of inertia in parallel axes`systems by Steiner theorem. However, look at what your doing, because maybe you need to place the system in a odd position.

Don`t forget to use vectors. Angular moment, torque, angular velocity, should be expressed as vectors referring your coordinate system.

I hope this helps.

Alejandro





davidvn10
Ok so should I divide the mass of a person into any number of spheres and then use the sphere moment equation for each sphere and then add them up and that should give me an estimated total moment of the human body? I guess if you made the spheres all the same size it would easy to calculate but less accurate right?

All the information I am given is height and weight of the person, I mean I could use anthropmetrics to determine lengths of body segments but I think that is a little to much detail, and the problem is meant to be somewhat simple and not over analyzed. This is why I believe the accuracy is not much of a factor and a close estimate is sufficient.

What do you think about this approach? Will it work or am I still missing the big picture? Thanks again I appreciate your time.
Alej
Hmm...
Because you will use a sum only, is not that important that each ball has the same mass that the others.

The main thing you should care about, is make the set of balls represents a human body. Maybe the proportion between fingers and arm, or something like that, is too much. But the body has some general proportions, relative to head`s size, and I would consider them. The mass center shouldn`t be a problem. It´s about placing the balls symetrically, and force the position of the mass center to be approximately, where actually is. But this alone can lead to overweight on arms and legs, so there is where proportions come to play a role. Other thing you can do is take a ruler, or something graduated, and then take proportions (of mass) of the body parts of any friend. That should be faster than search in internet.
Also, the total weight must be the sum of the balls weight.
Eh...well...It`s about trying to get something similar to a human body, you have to model it, there are some constraint, but not a rule that must be followed from the beginning to the end. It would be great if you manage to get the volume ratios of differents parts, and then use it to approximate a mass distribution. But if you don`t want to do it, maybe somethings that look`s like a human is enough.
Note that you can guide yourself by volume ratios to get mass ratios if you suppose density as constant (that`s ok for what you`re doing).

To get the distances from the reference system to the human model, you can do this:
Make draws at scale (like an architect, maintain a constant ratio between your draw lenghts and areas, and the real model lenght and areas). Make draws of a frontal view, and you would need some other direction depending on how you placed the balls. Then use a rule, and get the distances, then use the scale fator.
Other method is to use a computer software, but it has to allow you to make the human model, and measure the distance from a reference system.
Other way is some analytical way. Can be pretty easy, but also would require some long calculations.
The last way I can think at this moment is that you set distance between balls, and then use some trigonometry to get diagonals an so. But take care, because force the system in this way, can produce bad models.

Then do the sum.
If you placed the axes in some symetriy axes, it`s probable that the matrix will be a diagonal one (all terms but the diagonal are null).

Good luck. Any question, only post smile.gif

Alejandro



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