Moment of Inertia of a Flat Disk

[Jacob Roman]

What's the moment of inertia of a flat disk? Thanks.

[Jacob Roman]

Is it 1/2 * m * r ^ 2 ?

[Jacob Roman]

Oh come on people, don't make this my umteenth thread that never got replys.

[kaZm]

Well... you answered your own question

1/2 m*r^2 is a theoretical value of the moment of inertia

[Jacob Roman]

But theres a lot of them that are different formulas. It depends on the geometry of the object.

[BobTheBuilder.]

Well for a cylinder its I = 1/4M*R^2 + 1/3M*L^2
...so for a flat disk I = 1/4M*R^2 makes sense!

[NoteMe]

Oh come on people, don't make this my umteenth thread that never got replys.

I moved it to the math section, since this is a math question, and will probably be better answered there...



Tell me if the topic changes to more game related questions, and we will move it back.


ØØ

[kaZm]

Well for a cylinder its I = 1/4M*R^2 + 1/3M*L^2

Hmmm.. Im pretty sure its 1/2, but I could be wrong.

I found this from google.
http://dept.physics.upenn.edu/course...v_05_1999.html

[Jacob Roman]

Yeah it's gotta be 1/2

[sciguyryan]

I asked this question to a riend of mine who is a mathematics and physics expert and he replied with this:

The moment of inertia of a solid is always associated with an axis about which it could rotate.

In everyday physical terms, it measures the effort required to accelerate the solid turning about the axis. A solid having a larger moment of inertia will take a longer time to spin-up when applied the same force compared to when applied to another object with a smaller moment of inertia. You get the idea when we borrow 'inertia' to mean the resistance to changes!

In structural engineering, it is used extensively to measure the rigidity of a sttructural member, such as a beam or a column to resist bending or buckling. The value is indispensable in calculating how much a beam will sag, or deflect, under load.

Coming back to moment of inertia, we will calculate the moment of inertia of a solid flat disk about an axis through its centre, and perpendicular to the flat faces of the disk. We will require calculus to achieve the calculations.


Imagine a solid to be subdivided into many small fragments, each of mass dm, the moment of inertia, Iz of a solid about the axis z, is defined as the sum of the elemental mass, dm, multiplied by the distance squared from the axis. In other words, (using the word sum to mean the Integral sign in calculus),

Iz=Sum[ r*r dm]

for a flat disk about the z-axis, Ix=(mr^2)/2 where m is the total mass of the disk.
For a flat disk about axes passing through each of the x and y axis in the plane of the disk, we have the relationship

Ix+Iy=Iz, whence Ix=Iy=Iz/2=(mr^2)/4.

This is a very, very simple view of the answer, but fortunately a lot of information is out there available, for example, to derive the moment of inertia, you could check up:

http://homepages.which.net/~paul.hil...MOIproofs.html

You could also look up how to calculate the angular velocity of a solid disk , deflections and bending of a cantilever beam, etc. to see practical applications of this very interesting mathematical quantity.

Hope that helps you

Cheers,

RyanJ

[krtxmrtz]

If it's about its rotation symmetry axis then it's 1/2 Mr², regardless of how flat it is. Unless by "flat" you mean a 2D disk, i.e. a circle, in which case the calculation can equally be done if you define a "surface density" as Mass/Area, but the physical meaning, if any, must be different. Still the result would be 1/2 Mr²

[Jacob Roman]

Is the radius measured in meters, centimeters, or kilometers?

[krtxmrtz]

Is the radius measured in meters, centimeters, or kilometers?

Whichever you prefer, nanometers, parsecs, millimeters, light-years... That depends on the object size. But if for example you want meters for something you can only visualize at the microscope instead of micrometers, then you'd have to use times 10 to the minus 6 or whatever.

[moeur]

Jacob,

Make sure that whichever units you use that you are consistent throughout the rest of your calculations.

Be safe and put all measures of length in meters, all mass into Kilograms, and all time in seconds (mks).

As stated above the moment of inertia you want is 1/2 M r^2 as already stated in one of your previous posts.
http://www.vbforums.com/showthread.p...hlight=inertia

I thought you bought a book?

[Jacob Roman]

I did but it didn't have the moment of inertia formulas of different geometric objects.

[krtxmrtz]

I did but it didn't have the moment of inertia formulas of different geometric objects.

If you know/learn how to solve simple integrals you'll never have to learn by heart any formulas.

[VBAhack]

http://www.algebra.com/algebra/about...rtia.wikipedia

VBAhack