Axis Definition and 927 Threads

The Axis powers, originally called the Rome–Berlin Axis, was a military coalition that fought in World War II against the Allies. The Axis powers agreed on their opposition to the Allies, but did not completely coordinate their activity.
The Axis grew out of the diplomatic efforts of Nazi Germany, the Kingdom of Italy, and the Empire of Japan to secure their own specific expansionist interests in the mid-1930s. The first step was the protocol signed by Germany and Italy in October 1936. Benito Mussolini declared on 1 November 1936 that all other European countries would from then on rotate on the Rome–Berlin axis, thus creating the term "Axis". The almost simultaneous second step was the signing in November 1936 of the Anti-Comintern Pact, an anti-communist treaty between Germany and Japan. Italy joined the Pact in 1937 and Hungary and Spain joined in 1939. The "Rome–Berlin Axis" became a military alliance in 1939 under the so-called "Pact of Steel", with the Tripartite Pact of 1940 leading to the integration of the military aims of Germany, Italy and Japan. As such the Anti-Comintern Pact, the Tripartite Pact, and the Pact of Steel were the agreements that formed the main bases of the Axis.Particularly within Europe, the term "the Axis" is still often used primarily to refer to the alliance between Italy and Germany, though outside Europe it is normally understood as including Japan.At its zenith in 1942 during World War II, the Axis presided over territories that occupied large parts of Europe, North Africa, and East Asia. In contrast to the Allies, there were no three-way summit meetings and cooperation and coordination was minimal, and on occasion the interests of the major Axis powers were at variance with each other. The war ended in 1945 with the defeat of the Axis powers and the dissolution of their alliance. As in the case of the Allies, membership of the Axis was fluid, with some nations switching sides or changing their degree of military involvement over the course of the war.

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  1. A

    The volume of a solid rotating about a different axis

    Homework Statement y = {\frac{1}{4+x^2}} on the interval [0,2], revolving about y = -1 Use either the disk/washer or shell method to find the volume. Homework Equations v = pi\int (outer radius)^2-(inner radius)^2\,dx v = 2pi\int (radius)(height)\,dy x = \sqrt{\frac{1}{y}-4}...
  2. R

    Spacetime diagrams: ct axis and time contraction and length dilation

    Hi, this isn't really a homework problem... but I'm just wondering I see the time axis as c*t, now people say that its to scale the time axis so that the world line of light is 45 degrees. But if you were to multiply time by the speed of light, wouldn't you just get the units metres or...
  3. T

    Vertical Axis Wind Turbine Power Estimation

    Hello, Can some explain to me how to calculate the power coefficient of a vertical axis wind turbine. If you explain the steps invloved would be great or any external file location where I could refer. I have below information 1) Lift Coefficient. 2) Drag Coefficient. 3) Angle of...
  4. Matt Benesi

    Rotation from axis to axis in 4 dimensions

    I can easily visualize the 3 dimensional way to do so, and already have. I'd like to rotate from the (-1,-1,-1,-1) -- (1,1,1,1) line to the x-axis (-1,0,0,0) -- (1,0,0,0). To do so in 3 dimensions (-1,-1,-1) -- (1,1,1) line to the x-axis (-1,0,0) -- (1,0,0) I rotated around the z...
  5. F

    Deriving the major and minor axis of an ellipse

    1. Deriving the major and minor axis of an ellipse from conjugate diameters pointsCurrent solution: double x1 = Diameter1.X - Center.X; double y1 = Diameter1.Y - Center.Y; double x2 = Diameter2.X - Center.X; double y2 = Diameter2.Y - Center.Y; double xc = (x2 + y1) / 2; double yc = (y2 - x1) /...
  6. C

    Find the moment about the and axis

    1. Homework Statement http://session.masteringengineering...bs._454_55.jpg Find the moment about the axis AC. F=<7,12,-6> 2. Homework Equations MomentAC = Uac dotted with (Rab X F) Uac is the unit vector from a to c 3. The Attempt at a Solution Uac=<.8,.6,0> Rab=<4,3,-2>...
  7. C

    Calculating Moment About Axis AC for a Given Force Vector

    Homework Statement http://session.masteringengineering.com/problemAsset/1127287/7/Probs._454_55.jpg Find the moment about the axis AC. F=<7,12,-6> Homework Equations MomentAC = Uac dotted with (Rab X F) Uac is the unit vector from a to c The Attempt at a Solution Uac=<.8,.6,0>...
  8. B

    Moment of inertia and force needed to tilt/change axis of rotation

    Consider a freely rotating body. Let the axis of rotation be the z-axis. For simplicity assume all the mass of the body is concentrated in the x-y-plane, i.e. the plane in which the body rotates. I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine...
  9. B

    Accelerationg of rotating mass *along* the axis of rotation

    Says Wikipedia: "The moment of inertia is a measure of an object's resistance to any change in its state of rotation". Now consider a rotating mass m that I would like to accelerate along its axis of rotation by a. Does this count as a "change in its state of motion"? Will it resist the...
  10. J

    Rotate a cylinder to allign axis

    Hi i have cylinder geometry . bottom (cross section)circle centre point is x1, y1, z1 and top is x2, yz, z2. cylinder centre axis is not allign with any (Global x,y,z) axis. if i want to align a cylinder with Global axis(x,y,z), what is angle need to rotated with respect to x ,y ,z (Global )axis.
  11. U

    Magnitude of moment about axis (Space Truss)

    Homework Statement Determine the magnitude of the moment of the force F about the axis CA of the tripod ABCD, if F = {40i -30j -100k}N. Image attached. 2. The attempt at a solution Based on a similar question I found in the textbook my method to solve this question: Find UCA =...
  12. M

    What Does Rotating a Circular Arc Create?

    A 180 degree circular arc (i.e. a half sphere) is obvious: When you rotate this about its two end points, you get a sphere. What about for something less than 180 degrees (e.g. 90)?: I believe this forms an ellipsoid, with coefficients a and b being equal, with respect to...
  13. A

    Simple argument that a force applied farther from the rotation axis

    Torque is defined as: τ = rxF this means that the farther from the rotation axis of a body a force is applied, the more it will tend to rotate the body. My question is: Can anybody give me a simple argument that a force applied farther from the rotation axis should be better at...
  14. K

    Rotational Dynamics about an axis parellel to the axis at the center of mass

    Homework Statement A uniform sign is nailed into a wall at its top two corners. The nail on the upper-right corner breaks, and the sign begins to rotate about the remaining nail in the upper-left corner. The mass of the sign is 69 kg, L (length) = 1.6 m, H (height) = 2.2 m, and the moment of...
  15. B

    Partial Derivatives with Respect To Lines That Are Not In The Direction of Axis

    A 3-dimensional graph has infinite number of derivatives (in different directions) at a single point. I've learned how to find the partial derivative with respect to x and y, simply taking y and x to be constant respectively. But what do I do if I want to take the partial derivative with respect...
  16. N

    Inertia with the parallel axis theorem

    Homework Statement A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center? Homework Equations Ip = Icm + Md2 Isolid sphere = 2/5MR^2 The Attempt at a Solution This is...
  17. L

    Plot Negative Axis Upward in Origin - Q&A

    Not sure if this is the right place to post it. Does anyone know how to plot negative axis upwards on Origin?
  18. T

    Solving inclined plane in different axis.

    I can work out the acceleration of a block that will take along the plane when the axes are the ones along and perpendicular to the inclined plane. But, when I choose a horizontal and vertical axis I end up with the same mistake as this guy in this thread did...
  19. P

    Zeros, x intercepts, passing through x axis or just touching it.

    Homework Statement Homework Equations The Attempt at a Solution So this isn't a specific question, I'm just having trouble with my definitions. In my book for f(x) = (x - 2) ((x + 1)^2) (x-4) it says that the zeros are at x = 2, -1, 4. On the page it shows that the graph doesn't cross the...
  20. N

    Atomic Physics: Quantization axis

    Homework Statement Hi I have a question - it is not homework, but something I have thought about for a long time. I really can't come up with a solution to the problem, and it is driving me crazy. Here is the problem: Say I have a linearly polarized monochromatic wave incident on an...
  21. J

    Projectile Motion: Initial Speed and Maximum Height Calculations

    A vertically moving object projectile reaches a maximum height of 50 meters above its starting position What is the projectiles initial speed? What is the height above the starting point at 3.3 seconds?
  22. T

    Another volume of revolution around x axis

    Homework Statement Find the volume of the area bounded by y^2 = 4ax and x=a rotated around the x-axis. Homework Equations integral of pi R^2 dh The Attempt at a Solution I just don't know how to handle the x=a part of the boundary. Any hints? thanks
  23. S

    Why Does the Integral Equal Zero in Parallel Axis Theorem Proof?

    Note: The following are taken from Physics for Scientists and Engineers 6E http://img542.imageshack.us/img542/821/75796098.png http://img152.imageshack.us/img152/5615/70724407.png http://img804.imageshack.us/img804/6813/65815357.png I don't really understand why is that integral...
  24. T

    Finding volume of area revolved around x axis

    Homework Statement The area bounded by the x-axis and curve y = 4-x^2 is rotated about x-axis, find the volume.Homework Equations [integral] pi y^2 dxThe Attempt at a Solution the answer is supposed to be 512/15 pi
  25. Saitama

    Instantanoeus axis of rotation

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  26. A

    Total energy of system along axis

    Its stated that total energy of an isolated system is given by E = \frac{1}{2}mv^{2} + \frac{1}{2}Iω^{2} + mgh. Whats the correct form when the velocity is along 2 axis, that is, along x and y-axis like v = (2, 1)? Should the resultant be taken or just add the kinetic energies along each axis...
  27. T

    Determine the problem of this force along the 2 axis of the pole

    Sorry if i post this one in wrong thread, But can you help to solve this one? so i can review or study it by my own.. :D thanks!
  28. L

    Defining an ellipse with the major axis and a point

    Hello! I'm not sure this is the right place to ask, but i have a huge problem. I have an axis and it's origin, and also a point. I suposed that is enought to describe an ellipse, but how to do so? I want to describe it by having it's center and both it's radius. Some images to ilustrate what I...
  29. ferret_guy

    Tracking Distance on one Axis with an Accelerometer

    I need to track Distance on one Axis with an Accelerometer for a rocket project (i know there are bettor ways t do this but i am dead set on this one) I was thinking as follows, Read Accelerometer Accelerometer*Δt=Δv Current speed+Δv=New speed distance+New speed*Δt=New distance
  30. M

    How Do You Define an Axis with Three Unit Vectors?

    Hello, I'm trying to define an axis as a set of 3 unit vectors--u, v, and w. at a given point P Suppose we are given the following vector u. From this vector u, we must define a plane such that u is normal to the plane. This plane will be represented by two perpendicular vectors v and w...
  31. N

    Can the Quantization Axis of an Atom Affect its Spectral Emission?

    Hi Please see the attached picture. It shows an atom, the filled black circle, which consists of a J=0 level (with m=0 sublevel) and J'=1 (with m' = +/- 1 sublevels). From the left is a nearly monochromatic laser impinging on the atom, which is linearly polarized along the same direction of...
  32. A

    Simpson's Rule to find the volume of f(x) rotated about the x and y axis.

    Homework Statement Answers in the back of the book about x-axis= 190 about y-axis= 828Homework Equations Simpson's Rule: (dx/3)* sum of(sequence of coefficients {1,4,2...2,4,1}*sequence of function values{f(0), f(1), f(2)...f(n-2),f(n-1), f(n)}) Volume using Shells: 2π ∫ (radius)(height) dx...
  33. I

    Planetary Axis Stability: Examining the Role of Moons and Other Factors

    All of you may have heard this. Without the Moon, Earth's axis would fly wildly out of control due to the other planets' gravity. Now, that makes sense, the Moon giving a stabilizing effect. But what confuses me is why Venus and Mercury both have near 0 degrees of tilt. They don't have a moon to...
  34. E

    Rotational Motion- Parallel Axis Theorem?

    Homework Statement A meter stick is held to a wall by a nail passing through the 60-cm mark. The meter stick is free to swing about this nail, without friction. If the meter stick is released from an initial horizontal position, what angular velocity will it attain when it swings through the...
  35. P

    Mie scattering of infinite cylinder (light parallel to axis)

    I've been reading a few books on scattering of light from particles, in particular mie scattering of cylinders. At first I want to look at infinite cylinders, then finite cylinders once I understand a bit better. The problem is that all of the books I've looked at treat the problem where...
  36. T

    Non-standard Beam Bending Question - Parallel to Neutral Axis

    Hi there, first post on these forums. I have a seemingly simply question about beam bending. We (mechanical engineers) are all very familiar with the standard beam bending scenario. The beams are always shown being loaded perpendicular to the neutral axis, regardless of the type of support...
  37. Y

    How to Calculate the Axis of Rotation in 3D Space?

    hey guys, I have a problem I need to solve for my masters thesis. I have an object that rotates in 3D space. There is no translation. Given that I have coordinates of one landmark at 2 instances of time I need to calculate axis of rotation and angle of rotation. is this sufficient...
  38. M

    MATLAB Change X & Y-Axis Scale in MATLAB

    Hi, how can i change x and y-axis scale to make sure that x and y-axis are on the same scale in matlab? my x-axis is from 0 80 but the y-axis is from -3 to 5, so in plot the axis are not the same but i want to have same scale on both axis. Thank you.
  39. K

    How to calculate spinning disc torque which resists tilting of the disc's axis?

    Hello, From what I've read, I understand that a spinning disc has a torque which resists the tilting of the disc's axis. From what I understand, the higher the angular velocity of the disc is, the more the disc will resist tilting. Can anyone tell me how to calculate this torque? If there is...
  40. H

    Rotation of free solid object in vacuum, location of axis of rotation

    Hi, I would be happy if you could solve and explain following problem: Imagine some solid long object (wooden plank for example) being just like that in vacuum, free, without being fixed to any point of space. Then, imagine only one forse pushing this object in a certain point of object...
  41. E

    Taking moments about which axis?

    Why doesn't taking moments about an axis passing through point A or B work? Why must it be the center of mass here?
  42. M

    MHB Finding the vertex, y-intercept and axis of symmetry

    I am lost and confused. I have been on the same problem for 2 hours. I know all the formulas, but I'm not doing something right...
  43. K

    Complex Integration - Poles on the Imaginary axis

    Homework Statement evaluate the integral: I_1 =\int_0^\infty \frac{dx}{x^2 + 1} by integrating around a semicircle in the upper half of the complex plane. Homework Equations The Attempt at a Solution first i exchange the real vaiable x with a complex variable z & factorize...
  44. J

    Rotation of a body around which axis

    When i apply torque on a body, it will rotate around whcih axis? I guess its the axis along centre of mass but i don't know why? Also if the answer is centre of mass what will be the orientation of the axis- I mean there are infinite lines passing through a single point so which of those...
  45. L

    Moment of inertia of disk about off centre axis

    Homework Statement Find the moment of inertia of a uniform disk of mass m and radius r about an axis normal to the disk, through a point x from the centre. Homework Equations The Attempt at a Solution Let ρ be the density. I=ρ∫r^2 dA=ρ∫∫r^3 dr dθ in polar coordinates. However I...
  46. T

    How does phase affect the Nyquist Diagram - imaginary axis, how should it look?

    Please consider http://gyazo.com/e5c5b4f7808a63e7e664440259ac3058 I agree with all notes made on that slide, but I don't actually get how they constructed the diagram from that? I understand that they line represents frequency so going to 0 to infinity means the line would travel from -0.5 to...
  47. X

    Inertia of body that is oriented at some angle from axis of rotation

    1. Problem I am attempting to model the dynamics of the system shown in the attached image. I have a DC Motor with two disks attached to it via springs and something similar to a servo horn. I have two questions. The first is how to determine the inertia of the disk and the spring about the...
  48. 2

    Find volume of solid rotated about X axis Washer method

    Homework Statement y=x^2+1 X in (0,1) Homework Equations formula needed integral (PI [f(x)]^2 DX in the F(x) just plug in the equation right? The Attempt at a Solution took anti deritive of the original problem and came out with PI[1/3x^3+X]^2 my answer is 5.58 am i on...
  49. F

    Moment of inertia - displaced axis

    Hi, I need some help, I have a system with 3 cylinders (I got the center of mass for the system). Now I need to calculate the moment of inertia for the system. I have tried to find some examples or general information, but they all show when the axis either is centered within the object or...
  50. H

    Drawing (not too simple) Cosine waves on the x and y axis.

    I have to draw cosine waves in relation to pattern formation for mathematical biology, for example, I have to plot things similar to these on the x-axis; cos( 2*pi*x / √5 ) from x= 0 to √5 cos( 3*pi*x / 2 √5 ) from x= 0 to 2√5 cos( 3*pi*x / 2 √(5/6) ) from x=0 to 2√5 And with the y-axis; cos(...
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