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.
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...
So I am having trouble with this one, I was wondering if an object could have more than one axis of rotation. More than one axis of rotation goes against what I think is possible until I thought about a coin, at which point I was stumped, if the coin was rotating in the way a coin rotates when...
Homework Statement
Hi,
I am working making a soccer game in a game engine and encountered a problem with calculating what velocity a ball has to be kicked into get from A to B.
the ball has to be passed (on a flat surface with friction coefficient of 0.35) from point A to point B, but since...
What does the first two equations mean? I can't make sense of the notations. Does it mean taking the x-axis to be parallel to one principal axis and the y-axis to be parallel to the other principal axis?
Source: http://hepweb.ucsd.edu/ph110b/110b_notes/node29.html
EDIT: I figured it out. They...
Hello,
First of all, I'm sorry since I bet there are quite a few threads about this but I still have a bit of a hard time wrapping the axes of the Minkowski diagram around my head.
I understand very well that, to have the speed of light traveling at a 45 degree angle in a space-time diagram...
Homework Statement
If a vector makes 45 degrees and 60 degrees with x-axis and y-axis respectively then the angle it makes with z-axis is equal to
Homework EquationsThe Attempt at a Solution
I have a velocity vector as a function of a latitude and longitude on the surface of a sphere. Let us assume I have a point V(lambda, phi) where V is the velocity. The north pole of this sphere is rotated and I have a new north pole and I have a point V'(lambda, phi) in the new system. I have...
Homework Statement
determine the second moment of inertia about the horizontal axis and vertical axis for the shaded area with respect to x and y axes through the centroid of the area .
Homework EquationsThe Attempt at a Solution
Since the x and y axes is drawn thru centroid , why not the y...
Homework Statement
Show that for a two spin 1/2 particle system, the expectation value is \langle S_{z1} S_{n2} \rangle = -\frac{\hbar^2}{4}\cos \theta when the system is prepared to be in the singlet state...
I'm almost there in terms of understanding it, but I need to go beyond the text.
Here is the example problem:
imgur link: http://i.imgur.com/UMj55tF.jpg
I can see that where we have 1 = \vec{x}^T A \vec{x} = \lambda \vec{x}^T \vec{x} that 1=\lambda \vec{x}^T \vec{x} = \lambda ||\vec{x}||^2...
Homework Statement
In a certain system of units the electromagnetic stress tensor is given by M_{ij} = E_iE_j + B_i B_j - \frac12 \delta_{ij} ( E_kE_k + B_kB_k)
where E_i and B_i are components of the 1-st order tensors representing the electric and magnetic fields \bar{E} and \bar{B}...
I'd like to prove the fact that - since a rotation of axes is a length-preserving transformation, the rotation matrix must be orthogonal.
By the way, the converse of the statement is true also. Meaning, if a transformation is orthogonal, it must be length preserving, and I have been able to...
we know that in the cartesian plane, slope between two perpendicular lines is -1. but what about the x and y axis? if we find the slope between them it is not equal to -1. why is the slope between two perpendicular lines on the cartesian plane is -1 but the axes themselves do not behave such?
Homework Statement
It's a question I ask to myself. A support turns at ##w_0## and can accelerate. A disk on the support can turn around itself (side view) but at start ##w_1=0##. I done the experimentation with 2 wheels but I'm not sure about my tests. There is an angle between 2 axes:
The...
Consider two functions ##f\left(x, y\right)## and ##g\left(px, qy\right)##, where ##p## and ##q## are known. How can I plot the two functions on the same graph (i.e. the same axes)? The function ##f\left(x, y\right)## will have axes with values ##x## and ##y##, while the other will have axes...
Homework Statement
Consider an elliptically polarized beam of light propagating along the z axis for which the E field components at a fixed position z are:
Ex = E0cos(ωt) and Ey = E0cos(ωt +φ)
Find the major and minor axes of the ellipse in terms of E0 and φ and sketch the ellipse in the...
Homework Statement
[/B]
Statement: Find the principal axes of the section shown:
The origin is on the top left corner.
Homework Equations
[/B]
Centroid equations:
Second moments of area:
Mohr's Circle for I equations:
Coordinates
Centre
Angle from principal axes:
The Attempt at...
Homework Statement
Hey everyone, I'm horrible at physics so bear with me if it's a really easy question.
I was working a problem out, where I assigned my x-axis with cosine, and my y-axis with sine, like how I always thought it should be.
However, in the solution, they assigned sine for the...
I'm still very early on in my reading, so forgive me if this question isn't coherent. In the "historical introduction" section of the 1920 University of Calcutta translation of the original papers of Einstein and Minkowski available via the MIT online archive, mention is made of the fact that...
In my quantum mechanical studies, I came across the information that if you know an electron's spin on one axis, then you can not know its spin on another axis. For example, if you know that an electron is spin up on the z-axis, then apparently due to the Uncertainty Principle, you can not know...
Homework Statement
The teacher said it is possible to use an epicyclic gearing with no axis fixed but nobody use the gearing like that. I watched this video:
at time 42s it's possible to watch it. I have 2 questions:
1) Is it possible to used the epicycloidal train with no axis fixed ?
2)...
below the speed of light we experience one axis if time and three of space. So at the speed of light the space and time unify and we get 4 isotropic axes of spacetime. 4 identical dimensions. is this correct?
Hi guys,
I have a problem in which I have to resolve \vec{R} along two axes, a and b. However, those axes don't have a right angle between them (hence, non-standard). See the image below.
http://srg.sdf.org/images/PF/VectorHW.png
I believe I'm doing this correctly, however my textbook...
Homework Statement
THe x and y axes have been rotated about the origin through a 45 degree angle
to produce the X and Y axes.. Thus, a given point P (x,y) has coordinates in the first coordinate system and (X,Y) in the new coordinate system
The orignal equation is y=10sech(x).
What is...
Homework Statement
5x^3+10x^2+20x+15 is rotated through the angle 45 degrees to new xy coordinate system.Whats the equation to the coordinate system?
Homework Equations
The Attempt at a Solution
New X= xcos(theta)+ycos(theta) New Y=-xsin(theta)+ycos(theta)
Homework Statement
Show that the S' axes, x' and ct', are nonorthogonal in a spacetime diagram. Assume that t = t' = 0 when x = x' = 0. (Hint: use the fact that the ct' axis is the world line of the origin of S' to show that the ct' axis is inclined with respect to the ct' axis. Next, note...
Homework Statement
AB is homogeneous with mass of 180 kg, goes 1.2m in the page and is hinged at A and resting on aa smooth bottom at B. All fluids at 20 C. Find height of water that will result on 0 force at B
Homework Equations
M_s = \int\int_s \ (\vec{r} \times \hat{n} )PdA...
I am using the displaced axis theorem:
\hat{I}=\hat{I}com+M\hat{A}
where \hat{A}can be represented as a matrix, the elements of which are determined by:
A_{\alpha\beta}=|Rc^{2}|δ_{\alpha\beta} - Rc_{\alpha}Rc_{\beta}
I know that it is derived from substituting in rk=rk'+Rc into the...
I am trying to attain the parallel axis theorem from the displaced axes therom.
I have the displaced axes thorem stated in this form:
\hat{I}=\hat{I}com+M\hat{A}
-Where Rc is the position of the centre of mass position-
-Where \hat{}is the inertia tensor of a rigid body wrt to rotations...
Ok, so the system consists of two massive spheres, m1 and m2, of radii a and b respectively, connected by a massless rod of length R, as seen in the diagram attached.
The question is to calculate the moment of inertia tensor.
Sol:
Set the origin at the centre of mass . So that we are in...
Homework Statement
Calculate the moment of inertia of a uniform, solid cylinder about it's perpendicular axes. The cylinder has length L, radius R, and total mass M. It is centered on the origin with the z-axis running through the center of it's circular faces.
Homework Equations
I =...
Hi everyone, :)
Here's a question with the summary of my method of how to solve it. I would really appreciate if you could go through it and let me know if there are any mistakes with my approach. Also are there any easier methods?
Problem:
Find an orthogonal transformation that reduces the...
Inertia -- Moments of Inertia of a rigid body (different axes)
Here is the problem http://imgur.com/pL6Bdgw
So I missed class today because I was studying for a genetics test. I don't need the answer or anything but I was wondering what the general rule for inertia that I would use for...
I figured out that θ is 30 degrees. After simplifying I still could not eliminate the xy-term: I ended up with:
10x2 - 6xy + 10y2 + 3(sqrt(3))x2 - 3(sqrt(3))y2 -32 = 0
note: the x and y terms above are in prime form (I just don't know how to show that on a forum)
As you can see I still have a...
Homework Statement
I'm asked to solve the typical intro level box on an inclined plane problem but I need to do it using the lagrangian.
My difficulty with it is that the axis I am required to use are not the typical axes used when solving this using Newtonian mechanics. Instead of the...
σx|x>=+|x>
σx|-x>=-|-x>
These equations also follows for σy and σz corresponds states |y> and |z>.
if we measure along axis X then X state vector let it go which means up spin and opposite not go through which means down spin.
and also same for y and z axis.
But,
σx|u>=|d> σx|d>=|u>...
" If a plane has more than 2 principal axes (axes of symmetry ) through a point, then every axis through that point must be a principal axis "
I can understand above statement regarding a circle, but square also has more than 2 principal axes, how can it be true for every axis of a square or a...
So I have been trying to figure out some orientation data that I gather from a triaxial gyroscope, and figure out my orientation using only initial conditions and angular velocity from the gyroscope's current axes.
The data is all relative to the current orientation, so if I rotate the device...
Homework Statement
The two small spheres of mass m each are connected by the light rigid rod which lies in the x-z plane. Determine the mass moments of inertia of the assembly about the x, y, z axes.
I have attached an image of the question
Homework Equations
The Attempt at a...
Hi everyone, I'm real confused and stucked about a point in applying Nyquist stability criterion... now i'll explain why.
I know that it's needed to know how many times I'm wrapping the nyquist critical point (-1;0) with my plot, and I'm enough good to draw by hand a nyquist plot, but the...
A lot of below might be a question of semantics however it helps to understand better, I am a novice:
1. What's the difference between a field and a dimension?
A field is present at all points in time and space, ...so is a dimension.
why don't we call/label a field as a dimension?
2. or...
Homework Statement
Shafts A and B connect the gear box to the wheel assemblies
of a tractor, and shaft C connects it to the engine. Shafts A and
B lie in the vertical yz plane, while shaft C is directed along
the x axis. Replace the couples applied to the shafts with a
single equivalent...
How to find that? In R3.
I want to rotate everything around a vector, at an angle A. (making a n openGL game at my free time)
I tried , for normalized vector V = <x,y,z>:
Displace V to start of axes.
angleToYZ = acos(y);
Rotate all around Z with that angle. (1)
angleToZ = acos(z)...
I am slightly confused by the labelling of the vertical axis on parton distribution function plots.
Take the one here: http://www.hep.phy.cam.ac.uk/~wjs/partons2008nlo.jpg
as an example.
The vertical axis is labelled as xf(x, Q^2), where f is the probability density of finding a...
Homework Statement
Homework Equations
The Attempt at a Solution
I am just trying to figure out how to start the problem. Any help would be greatly appreciated.
Let natural numbers N,M be fixed such that 1\leq M < N. If x\in\mathbb{R}^N is some vector, and V\subset\mathbb{R}^N be some subspace with \textrm{dim}(V)=M. How likely is it, that x+V intersects the axes \langle e_1\rangle,\ldots, \langle e_N\rangle somewhere outside the origin?
I mean that...
I'm getting conflicting information on the proper form of Mohr's Circle for the stress of a system at a rotation from nominal.
Actually it seems that Mohr's Circle is not a tool for just stress or moment if area/stress calculation, but in general for a 2-D simple symmetric form eigenproblem...