# IA (HL) Is my topic approrpiate/good for a Higher Level maths IA?

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I'm finally starting to come down to what I think my topic for my maths IA will be, but I need a little bit more. I'm looking at moments of inertia, potentially to calculate the moment of inertia felt by the propellers on a quadcopter I'm building. I'm not sure if the mathematics are "higher level" since I still have to learn quite a bit about moments of inertia, so I don't exactly know what mathematics (other than integral calculus) I would be using. So, is this topic a good start? How should I start developing it to get a focused research question for my IA?

Thanks for any help!

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I'm finally starting to come down to what I think my topic for my maths IA will be, but I need a little bit more. I'm looking at moments of inertia, potentially to calculate the moment of inertia felt by the propellers on a quadcopter I'm building. I'm not sure if the mathematics are "higher level" since I still have to learn quite a bit about moments of inertia, so I don't exactly know what mathematics (other than integral calculus) I would be using. So, is this topic a good start? How should I start developing it to get a focused research question for my IA?

Thanks for any help!

okay, so I have absolutely no idea of what the "moment of inertia" is  BUT as a general rule, if it has integrals in it, it will probably be commensurate with the level of the course. In the SL syllabus they only do integrals with substitution, so any trig-substitution or integration by parts is already HL. Keep in mind that even if your math isn't the most complicated thing, you can still earn quite a few points, and that if your math is too complicated you might have trouble explaining what you're doing and lose points in the communication criterion. Try to keep the "complicatedness" and the "communication" balanced.

As for the topic being a good start or how to get a focused research question, I can't help much, since I don't know what that topic is. But I hope this helped.

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I'm finally starting to come down to what I think my topic for my maths IA will be, but I need a little bit more. I'm looking at moments of inertia, potentially to calculate the moment of inertia felt by the propellers on a quadcopter I'm building. I'm not sure if the mathematics are "higher level" since I still have to learn quite a bit about moments of inertia, so I don't exactly know what mathematics (other than integral calculus) I would be using. So, is this topic a good start? How should I start developing it to get a focused research question for my IA?

Thanks for any help!

Before starting moments of inertia, you should first be more familiar with center of mass (including the geometric treatment, not calculus treatment), axis of rotation, and some experience evaluating simple integrals and derivatives. KhanAcademy and doing some exercises are good start in both the physics and the math.

Im not sure how far you are in building your helicopter, but it is not necessary to be this "engaged" to score the personal engagement part. This is not a woodshop/building course, IB wants you to engage mathematically, not physically. I do, however, encourage you to be engaged in your learning and not just go for the marks.

The calculus covered in IB is sufficient to find moment of inertia for a uniform-density (a plastic helicopter would not be if it uses various types of materials) 2-D object or 3-D object of revolution (something that has infinite vertical planes of symmetry, such as a vase), or possibly combination of the two. Area and volumes of revolution are typically the last topics covered in the core HL syllabus. This is a great topic for an IA provided that you have enough physics and calculus knowledge at time of writing the paper.

The definition of moment of inertia, integral of r^2 dm is easy to formulate but hard to evaluate in practice. The more straightforward formula for moment of inertia (used for non-uniform-density objects) involves double and triple integrals, which are way beyond the scope of HL Math. To learn double and triple integrals, you should be familiar with vectored-valued functions, quadratic surfaces/3-D plots), simple/x-simple/y-simple/elementary regions, iterated integrals, vector fields, scalar fields: none of these are covered in HL Math. So in your research if you see two or three integrals signs side by side, those are double or triple integrals and you are probably not ready for those yet.

So once you find the moment of inertia, you may choose to do some physics experiment to test your findings, such as using the the Second Newton's Law for Rotation. A lot of physics studying (less than for double/triple integrals) may be required to experimentally determine your moment of inertia, but I don't think it's necessary. It's a good way to know if your math is correct.

Edited by kw0573

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