What is Axes: Definition and 181 Discussions

An axe (sometimes ax in American English; see spelling differences) is an implement that has been used for millennia to shape, split and cut wood, to harvest timber, as a weapon, and as a ceremonial or heraldic symbol. The axe has many forms and specialised uses but generally consists of an axe head with a handle, or helve.
Before the modern axe, the stone-age hand axe without a handle was used from 1.5 million years BP. Hafted axes (those with a handle) date only from 6000 BC. The earliest examples of handled axes have heads of stone with some form of wooden handle attached (hafted) in a method to suit the available materials and use. Axes made of copper, bronze, iron and steel appeared as these technologies developed.
The axe is an example of a simple machine, as it is a type of wedge, or dual inclined plane. This reduces the effort needed by the wood chopper. It splits the wood into two parts by the pressure concentration at the blade. The handle of the axe also acts as a lever allowing the user to increase the force at the cutting edge—not using the full length of the handle is known as choking the axe. For fine chopping using a side axe this sometimes is a positive effect, but for felling with a double bitted axe it reduces efficiency.
Generally, cutting axes have a shallow wedge angle, whereas splitting axes have a deeper angle. Most axes are double bevelled, i.e. symmetrical about the axis of the blade, but some specialist broadaxes have a single bevel blade, and usually an offset handle that allows them to be used for finishing work without putting the user's knuckles at risk of injury. Less common today, they were once an integral part of a joiner and carpenter's tool kit, not just a tool for use in forestry. A tool of similar origin is the billhook.
Most modern axes have steel heads and wooden handles, typically hickory in the US and ash in Europe and Asia, although plastic or fibreglass handles are also common. Modern axes are specialised by use, size and form. Hafted axes with short handles designed for use with one hand are often called hand axes but the term hand axe refers to axes without handles as well. Hatchets tend to be small hafted axes often with a hammer on the back side (the poll). As easy-to-make weapons, axes have frequently been used in combat.

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  1. U

    I Why are rotated parallel axes still parallel?

    I tried posting this on the physicsstackexchange, but wasn't making any progress in understanding what's going on. Suppose the axes in two coordinate systems S, S' are parallel. Now, suppose I rotate S through some angle ##\theta## and also rotate S' through the same angle ##\theta## It's not...
  2. G

    Is Moment of Inertia Dependent on Surface Movement Away from Axis?

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  3. L

    Inertia tensor around principal Axes part 2

    Hi, it's about the task e) Since the density is homogeneous, I have assumed the following for ##\rho=\frac{M}{V}##. I then started the proof of ##I_{23}##, the integral looks like this: $$ I_{23}=\int_{}^{} -\frac{M}{V}r'_2r'_3 d^3r$$ Now I apply the transformation $$ I_{23}=\int_{}^{}...
  4. L

    Inertia tensor around principal Axes

    Hi, unfortunately, I am not getting anywhere with the following task The inertia tensor is as follows $$\left( \begin{array}{rrr} I_{11} & I_{12} & I_{13} \\ I_{21} & I_{22} & I_{23} \\ I_{31} & I_{32} & I_{33} \\ \end{array}\right)$$ I had now thought that I could simply rotate the...
  5. D

    I Are the coordinate axes a 1d- or 2d-differentiable manifold?

    Suppose $$ D=\{ (x,0) \in \mathbb{R}^2 : x \in \mathbb{R}\} \cup \{ (0,y) \in \mathbb{R}^2 : y \in \mathbb{R} \}$$ is a subset of $$\mathbb{R}^2 $$ with subspace topology. Can this be a 1d or 2d manifold? Thank you!
  6. S

    Moment of inertia of T bar about 3 axes

    Using the equation above I get Xcm = 0.022 m. I set the origin be at the left of the vertical rod parallel to its centre of mass as in the diagram. But I’m not sure if the equation is correct for 3d. for the moments of inertia I am using I = Icm + md^2 = (mr^2)/2 + md^2 where d is the...
  7. A

    I Rotation of a vector along two axes (of which one is angle-dependent)

    I have been trying to determine an expression for a unit vector in the direction of F for hours now. I think the expression is supposed to look something kind of like this, But I don't understand at all how to arrive at this expression. Any help?
  8. DaveC426913

    B Artificial gravity rotating on two axes

    The world building thread about a derelict spaceship got me wondering. An object can rotate on two axes simultaneously, yes? Is that stable in flat space? If so, what would occupants experience as gravity? Would it change over time?
  9. A

    Trouble Understanding Hinge Axes: Ax ≠ Bx?

    I am confused by the drawing of the door with hinges A and B attached. I do not understand why -Ax = Bx. I would have thought that Ax = Bx
  10. Reinhardt Walzer

    I Time Dilation along Multiple Axes

    Been studying Special Relativity in Uni. and I've noticed that all examples of relativistic motion provided are motions only along a single axis, like the one below: The particle's Reference Frame is moving only along the X axis in the example above. In this case the Lorentz Transformation for...
  11. Monsterboy

    Vectors along different coordinate axes

    The answer in the textbook are options A, C and D. I understand why it is option A, because it is a scalar, I also get that option D is correct because the magnitude of a vector doesn't depend on the coordinate axes. I don't get how option C could be correct. If option C is correct why not D as...
  12. FactChecker

    B Comparing Approaches: Linear Regression of Y on X vs X on Y

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  13. K

    I Rotation about two axes and angular momentum

    I've a body having initial angular velocity at ## t=0 ## as shown. The axis shown are fixed in inertial space and initially match with the principal axis. I want to find the infinitesimal change at ##t+\Delta t## in the angular momentum along the ##z## axis. I've seen the following approach...
  14. K

    I Trying to rotate a disc about two perpendicular axes

    I've a disc which can rotate freely about two perpendicular axis (fixed to the body) If I simultaneous try to rotate it about the two axis, what will happen?
  15. K

    I Axes of the 2-d coordinate system used in vector resolution

    Hello, This question is with regards to the discussion around page 56 (1971 Edition) in Anthony French's Newtonian Mechanics. He is discussing the choice of a coordinate system where the axes are not necessarily perpendicular to each other. Here is the summary of what I read (as applied to...
  16. P

    Velocity addition formula in X and Y axes (Relativity)

    The problem: Visualising the problem (My question is with regards to this): Why is the above set-up correct? In the above diagram, S would be moving at velocity -v relative to S', instead of v. Is this because the question says "speed v", and so we can set the direction as such? Why would the...
  17. Leo Liu

    Stability of rigid body rotation about different axes

    We know that for a non-rigid body, the most stable type of rotation of it is the rotation about the axis with the maximum momentum of inertia and thus the lowest kinetic energy. However, for this question involving a rigid body, the most stable axis is the one with the lowest moment of inertia...
  18. wcjy

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    $$B = \frac {\mu_0 I}{2 \pi r} $$ By Right-hand Grip Rule, the direction of the magnetic field by wire in y-axis is into the paper (z) while the direction of the magnetic field by wire in X-axis is upwards (+i) The answer state the Magnetic field is in the (i - y) direction though. Next...
  19. mingyz0403

    Engineering Moment of forces about the axes

    I reslove Ma and Mb into y and z component. Ma=1200sin(20)j+1200cos(20)k Mb=900sin(20)j+1200cos(20)k Mc=-840i I looked at the solution and it states that the y component of Ma is negative (-1200sin(20)j+1200cos(20)k). I understand that Mc is -840i because it is Clockwise. How do you determine...
  20. Daniel Lima

    Python How to plot a function with multiple parameters on the same set of axes

    I attached a file with some explanations of the variables in the code and the plot that I should get. I don't know what is wrong. Any help will appreciated. from scipy.integrate import quad import numpy as np from scipy.special import gamma as gamma_function from scipy.constants import e...
  21. E

    Bending moments about two different axes

    I was reading through a set of notes and found something a little odd. The aim is to solve the beam structure shown below, which is massless and of length ##l##. By considering the beam as a whole, we obtain ##A_y = P##, ##A_x = N## and by taking moments about A we see ##M_A = Pl##. However...
  22. Grinkle

    B Meaning of Time / Space axes swapping (for Time)

    I am including a link to a B level discussion of this I found on-line to try and anchor my question, not because I think the below article is good or poor - I am not able to assess that. https://www.einstein-online.info/en/spotlight/changing_places/#The_analogy In particular I am asking about...
  23. O

    I Coordinate Systems After Deformation of Axes

    Disclaimer: I am a physics student and I have very little knowledge of topology or differential geometry. I don't necessarily expect a complete answer to this question, but I haven't really found any reference that approaches what I'm trying to ask, so I'd be quite happy to simply be pointed in...
  24. AzureSekki

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  25. C

    B How can a dimension be "curled up" and have a finite extent?

    As I understand it, dimension is a way of describing direction, with the first three spatial dimensions being straight lines which extend infinitely in one direction, perpendicular to each other. In string theories, several additional dimensions are required, sometimes up to nine or 10, I...
  26. L

    Rolling without Slipping - axes of rotation and centripital acceleration

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  27. RichardWattUK

    I Translating points on the axes

    Summary: I need to translate points on coordinate axes as part of a calculation process Hello everyone, I've created the diagram below to try and explain what I am trying to do as part of an existing software app that's used to generate profiles and programs to drive a CNC machine to grind...
  28. peguerosdc

    How to relate the gravitational potential energy zero to the axes?

    (Throughout all my post, I will refer to “gravitational potential energy” just as “potential energy”) Hi! I have this confusion about when is potential energy positive/negative and how it is related to how we define our axes. I think it is easier to understand my confusion with the following...
  29. I

    Forces along non-perpendicular axes

    Determine Force from F2 along u and v axes. CompF= F*Cos(angle); CompF onto U = 8kN*Cos(30) = 6.93kN Angle between F2 and V: 180-75 = 105; 105-30 = 75 degrees CompF onto V = 8kN*Cos(75) = 2.07 kN. Since in the -V direction; -2.07kN. I just would like for somebody to verify these answers. I've...
  30. J

    B Correlation between shifting graph of a function and shifting the axes

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  31. Ventrella

    I Iterating powers of complex integers along axes of symmetry

    I am exploring the behaviors of complex integers (Gaussian and Eisenstein integers). My understanding is that when a complex integer z with norm >1 is multiplied by itself repeatedly, it creates a series of perfect powers. For instance, the Gaussian integer 1+i generates the series 2i, -2+2i...
  32. Avi Nandi

    I Space & Time Axes Coinciding: Consequences Explored

    Let's consider two inertial frame S and S'. S' moves with speed v w.r.t S along x-axis towards the right. Now we can draw the two co-ordinates system. The t' axes will make an angle arctan(v/c) with t axes rotated towards x-axis and similarly the x' axis will be tilted towards the t axes...
  33. C

    MHB Calculus III: Proving Tangent Line = 1 for Every Point on Curve

    Hi, I'm stuck on a homework problem in my Calculus III class. I solved 3a really easily, but 3b is giving me a lot of trouble. I know that to find the tangent line, I first have to find the slope, which is represented by the vector: <3cos^2(t)(-sin(t)), 3sin^2(t)(cos(t))>. I know the formula...
  34. kasoll

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    Is there a method to calculate inertia tensor form principal axes moment of inertia? Like now we have moment of inertia: (Ix,Iy,Iz)=(20,18,25), and hot to calculate the inertia tensor like (Ixx,Ixy,Ixz Iyx,Iyy,Iyz, Izx,Izy,Izz)? I have read about this page several times, but still have no idea.
  35. L

    I Generalizing the Bell Inequality for Arbitrary Measurement Axes

    EDIT: I realize now that I have fundamentally misunderstood a crucial aspect of deriving the Bell inequality for this case which is the existence of the third axis. The setup of the problem did state that the axes were chosen at random. Therefore I can't just look at the possibility of choosing...
  36. E

    Cube balanced at equilibrium about two different axes

    Homework Statement A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in _______ equilibrium with respect to rotation about the edge and in _________ equilibrium with respect to rotation about a horizontal axis that is...
  37. D

    I Understanding Quantum Mechanics: Equations for Spin Along x and y Axes Explained

    I am currently reading Leonard Susskind's "Quantum Mechanics the Theoretical Minimum". In chapter 2.3 and 2.4, he defines |r>, |l> and|i>, |o>, for r and l along the x-axis and i and o along the y axis. The equations are: $$|r> = \frac{1}{\sqrt{2}}|u>+\frac{1}{\sqrt{2}}|d>$$ Since...
  38. HydroMarioUSA

    How Does Friction Affect Motion on an Inclined Plane?

    See the screenshot for the full problem. 1. Homework Statement We're given a pulley with one side hanging (A) and the other on an inclined plane (B). We are also given that the mass of A is 15 kg and the mass of B is 17 kg. The angle of elevation of the inclined plane is 32 degrees. The...
  39. donaldparida

    Find the angle between this vector and the coordinate axes

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  40. Mind----Blown

    General approach to find principal axes of rotation?

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  41. S

    Inertia tensor of a body rotating about 3 axes

    Homework Statement Hello, I know about the inertia tensor about one axis, but how about a body that rotates around 3 axis x,y and z such as a spacecraft with changes in the attitude. Thanks for you help. Homework EquationsThe Attempt at a Solution
  42. R

    How do tires create momentum and change axes in a car turning right?

    A car traveling north makes a right turn, to head east. How do the tires completely offset py and simultaneously create px? (If the tires merely acted like guidance jets, it might turn to face east but continue traveling north.
  43. Const@ntine

    Aeroplane follows circular trajectory-Tension? (geometry)

    Homework Statement So, I have this problem here that's pretty basic, but the solution manual sets different axes, and I'm having a bit of trouble understanding the geometry part, meaning how he applies the given forces to the new axes. A model airplane of mass 0.750 kg fl ies with a speed...
  44. C

    Choosing different axes in the same system

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  45. C

    I Find potential integrating on segments parallel to axes

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  46. S

    I Monoclinic Cell Rotation for Surface Calculations

    Dear All, I have a monoclinic cell with a=18.7,b=3.55,c=9.069 and beta=134 degrees, angle between a and c. Now I need to make the c axis parallel to z axis for surface calculations, ie to introduce a vacuum. What is the rotation matrix that would do this?? Thank you.
  47. I

    Rotations around the x and y axes of stereographic sphere

    Homework Statement Show that the equations $$ \delta \phi = \cot \theta \cot \phi \delta \theta, \quad \delta \phi =- \cot \theta \tan \phi \delta \theta$$ represent rotations around the x and y axes respectively of a stereographic sphere. Both these two rotations map the sphere on itself and...
  48. G

    I Minkowski diagrams without scales on axes

    Hi. I have seen quite a lot of demonstrations of time dilation and length contraction that used standard Minkowski diagrams WITHOUT any scales on the axes at all. If I understand them correctly they seem to directly compare lengths, which would imply (I think) that the scaling on the ##ct/x##...
  49. L

    B Are the axes of celestial objects parallel in a galaxy?

    Speaking only of approximately spherical moons, planets, and stars (not asteroids), which rotate about their axis, are the axes all pointed approximately the same direction? Is it true for moons and their parent planet? Is it true for planets and their parent star (solar system)? Is it true for...