Explain this to me. I'm in Algebra II and taking 9th grade physical science. Ideally, an answer would come in the next hour so I could stick it in my paper due tomorrow, but that won't happen. By the way, Moose, Merrell, and Dapperdan, you guys are lazy. D:
WE ALL KNOW YOU DON'T REALLY SLEEP, DAPPERDAN!

I don't know why they don't use the term moment of inertia, because I think that's what this is.

Nobody here is your teacher, what needs to be explained?

What do you mean explain it to you? This is stuff that I am learning right now in my engineering mechanics class... (well actually I learned it a semester or two ago)

yes frazz it is moment of inertia

Explain how the math works in a relatively simple way. It's quite the daunting task.

Calculus, that's basically what it is...

Is your 9th teacher really making you write a paper about topics in Solid Mechanics? Because this is shit you learn in Engineering classes in college.

it's the difference between a full cylinder and a hollow one cylinder and rolling down an incline. Closer to center is easier to move.

Fatal, first of all do you know how to integrate or differentiate? Because that's the underlying math to calculating the moments of inertia

We have to build a cantilever wing beam from nothing but newspaper and starch capable of holding... Well, a lot. This is for a background information paper.

And no.

Yeah, there's pretty much no hope to understanding the math if you don't know calculus. Essentially, you are adding up infinitesimally small segments of the area, dA = xdy or ydx, and then multiplying each differential area by the square of its distance from the axis.

Not having taken an applicable physics class, though, I don't know why the evaluation of this integral would be significant. My guess would be something to do with the equivalent mass depending on where you apply the force, but just a guess... I also get the feeling that its also a degenerate form of something like I = ∫∫x²y² dA = ∫∫x²y²(dx)(dy). Just a guess though.

Is there a simple explanation of what differential area is, then? That's pretty much as simple as I expected it to get.

You don't need moments of inertia if you are simply designing a beam capable of withstanding loads, especially if you can't do calculus. You just need basic statics knowledge.

A differential area is infinitely small. The essence of an integral is that you add an infinite number of infinitely small pieces to yield a finite result. We call it the differential of area, dA (said "dee-ay") because it, in one case, has width x and differential (or infinitely small) height dy. The "short" side of the rectangle in the picture is actually infinitely small, but they want you to see it.

Of course I don't need it for building the thing, but I need it for the paper the comes first.
I kind of guessed that it wasn't actually that wide, so is it kind of like a plane that goes through, parallel to the upper edge with the the width defined as the object's width? (By the way, I have taken geometry)

I don't exactly know what your teacher wants you to talk about in your paper, but here's what I would write about.

- Newton's first law: equilibrium. This beam is going to have two opposite and equal forces: the Load of w/e weight, and the base of this beam is going to produce a normal force so that your beam actually stands (otherwise it'll crumble).
- Torque. I'm assuming that one side of your beam is going to be fixed to a rigid end and that the other side is free and that the load would be attached there. You also have to figure out the internal moment around the fixed end of the beam so that the summation of the moment about your whole beam is in equilibrium (otherwise your mean is going to succumb and collapse)
- Know the difference between compression and tension. These are both forces, but remember beams are two-force members, meaning their internal forces are axial and 1 dimensional. So Statically, their internal forces will either be pointing towards each other or away from each other (being tension and compression respectively). When making any beam, it is crucial to know which of these two forces are greater and to know whether the material used is capable of withstanding greater compression or torque
- Stress and strain. Stress is equal to the internal force of the beam over its cross sectional area (i.e. if your beam is a long circular tube, then the cross sectional area is pi*radius^2.) Not that you have to actually calculate the maximum stress newspaper can withstand, but when it comes to making any beam, understanding of the ultimate stress of any material is crucial in determining how safe your beam is going to be. Strain is the elongation per unit length. So it equals delta/original length. And to calculate delta, you have to know the internal force of the beam (and to calculate this, you have to figure it out through free body diagrams) and you have to know the modulus of elasticity of the material.
- Deflection, this is where when a beam is laterally loaded, the whole beam will be bent concave downwards (assuming that the load is vertically downwards). Again you have to know the modulus of elasticity of the material as well as its Inertia
- Trusses and joints. If the whole structure is going to use more than one beam, then there are going to be multiple trusses and joints. In order to calculate the internal forces of each beam, you have to a free body diagram around each joint and use newton's first law to calculate the forces of each beam. One must note the difference between x directional and y directional forces.
- Torsion is important. Torsion is the twisting force about a beam. Torque = Shear stress/radius of cross section of beam *polar moment of inertia. If the beam is circular, then the moment of inertia = PI*diameter^4/32. If the beam is hollow, then it's simply PI(D_outer^4-D_inner^4)/32. If the beam is a rectangle, then the moment of inertia is = bh^3/12. One must note whether this is the x or y directional moment of inertia. Also one must know about the righthand rule. When a torque is applied clockwise about a point, it points up, and vice versa. Like with forces, Torques must also be in equilibrium
- Since this class is physical science afterall, I would primarily talk about the properties of the materials that would be used. Like whether they are inelastic or w/e.



Post has been edited 1 time(s), last time on Mar 4 2008, 6:25 am by MillenniumArmy.

Here's what's supposed to be in it, by paragraph number (not exactly a long paper, either):
1: Factors that affect wing beam design
2: History of cantilevers
3: Evolution of wing beams from 1900-2000
4 - 5: Advantages and limitations of different wing structures (ex. monoplane, biplane)
6: Role of materials in wing beam design
7: Role of geometry in wing beam design
8: Forces acting on a wing beam during flight
9: Modes of failure
10: Reasons to continue wing beam research

3 and 6 are the only ones I didn't do, now. Surprisingly, I couldn't find anything on the exact materials used for wing beams.

I think I answered 6 for you. It deals with stress and strain of the beams. You just have to know that you need the modulus of elasticity of the material used. It is inversely proportional to the elongation of the beam when a load is applied to it.

but in response to DTBK's question earlier:
If you are simply dealing with straight edged or symmetrical objects like squares, rectangles, circles, etc then you normally are just given the equation for calculating the moment of inertia. However, like in calculus when you want to find the area under a curve, you have to integrate because height is a function of x or w/e (i forgot what the exact reasoning was for this). Same concept with polar moments of inertia. Whenever the boundary or borders of objects or shapes are given to you as a function of displacement, time, or even velocity, you always need to integrate because they are never constant. In beginning physics, when you learn mechanics, you are typically told that acceleration is constant or zero. However later on, it will not be constant and will become functions of another element.

Post has been edited 3 time(s), last time on Mar 4 2008, 6:47 am by MillenniumArmy.

If you didn't need calculus for this class, that's probably not what you should focus on.


High school can screw with the finest of sciences, even physics and *shudder* mathematics.

wtf? This isn't Physics, no r? wheres mass? WHATS RHO?!?!
what sort of moment of inertia is this?

Yeah, I was asking my dad who fished out a physics textbook and explained that the moment of inertia had to do with the angular momentum around a point, the moment being ∫ρr² dV, properly ∫∫∫ρr² dV if ρ and r are defined as functions of their position x, y, z.

Post has been edited 1 time(s), last time on Mar 4 2008, 3:36 pm by DT_Battlekruser.

Cartesian. Anything with x and y components is cartesian

Post has been edited 3 time(s), last time on Mar 4 2008, 7:37 am by MillenniumArmy.