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.
Homework Statement ?
How do i find a vector that has same angle with the three coordinate axes (x,y,z)?
The Attempt at a Solution
I immediately thought [1,1,1] would be it but it's not. I'm trying to find a plane whose normal vector forms the same angle with the three coordinate axes.
Dear All,
I have come across with a seemingly very simple problem but could not solve it by searching on internet and books. May be I am confused.
I want to rotate a 3D body around an arbitrary axis with fixed principal axes. The solutions I found is with Euler angles (Euler rotational...
Homework Statement
A right triangle is formed in the first quadrant by the x and y axes and a line through the point (1,2). Find the vertices of the triangle such that its area is a minimum.
Homework Equations
a=\frac{1}{2}xy
x^2+y^2=h^2
y-2=m(x-1)
p=x+y+h
p=x+m(x+1)+2+h...
I was given the equation: 2sqrt(2)(x+y)^2=7x+9y
I need to then:
a)Use rotation of axes to show that the following equation represents a parabola
b) Find the XY- and xy- coordinates of the vertex and focus
c) Find the equation of the directrix in XY- and xy-coordinates
Formulas...
Dear all,
We can rotate the local coordinates of the element so that the stress tensor becomes diagonal. The new coordinate system would be the principal stress axes of which are in fact the eignevectors of the stress tensor.
Once we have the eigenvectors ( which are generally orthogonal)...
What happens when you have equal mass that is spinning about a common x and y axes as well as at the same rate(rpm)?
Now I use the term mass, understanding that this is the same in a vacuum as well as within our gravitational field. I may stand corrected here.
I've often wondered about...
Homework Statement
If we have a cuboid like this one
*It won't let me upload the picture or include a link but if you Google cuboid its the first picture*
We know that the mas moment of inertia through the centroid is different for each face. So the yellow has the greatest mass moment of...
Homework Statement
I do not understand how the vector (1 -1 0)T represents the axis tangent to the disk at Q.
The Attempt at a Solution
Tried thinking in terms of simple vector addition, but just got another vector in the radial direction...
I mean, (1 -1 0)T is parallel to a tangent...
∫Homework Statement
Grr it got all got erased...This is a math problem that a student I tutor got wrong on his calculus test. I am having problems remembering what to do. I have looked up other problems, but the paraboloids seem simpler for some reason. Probably because someone is...
I am just reading an introductory text on Industrial Robotics.
It talks about 3 Major Axes and 3 Minor Axes and Yaw, Pitch and Roll.
I am still confused as to the need for the minor axes. You locate the gripper at any point in spaces, 3 axes should be enough right? So what's the need for...
Angular vel. and mom.--origins vs. axes
This is a conceptual question.
Angular velocity is measured with respect to an axis, correct?
Yet angular momentum is measured with respect to an origin, i.e. a point, correct?
For angular momentum problems where only the magnitude of angular...
I already asked this question on physics.stackexchange.com, but did not get the desired response. I am interested in the opinion of your community.
Picture an entangled pair of spin 1/2-spin particles with total spin 0. In the diagram, particle 1 of the pair is moving to the left (-y), and...
Yes, that is my problem. I could never reproduce in computer the scheme I learned in Computer Engineering graduation I am coursing. The way the teachers show and in some books, I never get into that result but I don't know if it is exactly impossible.
At this page in wikipedia...
Homework Statement
Rotation of axes to Eliminate the xy-term in a quadratic equation
3x^2 - 10xy + 3y^2 + 16 √2x - 32 = 0
2. The attempt at a solution
I do not know the method that should be taken to solve this sort of question. That is what I am looking for. If anyone can point me...
Homework Statement
17. xy = 2
The Attempt at a Solution
Do you see that step where they do the following:
√2/2 - √2/2 = my answer is 0
and they multiply that to
√2/2 + √2/2 = my answer is √2
So to me the answer is 0 * √2 = 0, but the book shows that that calculation = 2, then they...
Hello,
Background:
We have a machine with two rotational axes (b,c) attached to each other. By design the B axis is rotating about the Y-axis and the c-axis is attached on top of the b axis.
Ideally the axes are orthogonal but in practice they are not. However we can measure the directions...
Homework Statement
f is a function of two variables: y, z. I want to show that the gradient:
\nabla f=\frac{\partial f}{\partial y}\hat y + \frac{\partial f}{\partial z}\hat z
Transforms as a vector under rotation of axes.
Homework Equations
The rotation of axes:
A...
Homework Statement
As a small verification of a larger problem, I'm trying to determine how the dynamics of an inverted pendulum attached to a frictionless cart would behave.
The cart has no input force applied, so all horizontal movements would be due purely to the centrifugal+normal...
Hi,
Am plotting a graph and need to scale the axes so that i can take my range of 'x'-axis values from -1 to infinity.
I shall provide script, but i am using the ParametricPlot command.
ParametricPlot[tab2, {up, -1 + 10^-7, 10},
AxesLabel -> {"\[Rho]", "u'"}, PlotRange -> {{-1, 2}...
I found this problem in a book and am trying to answer it by myself.
1. Can you think of a body that has the same moment of inertia for all possible axes? If so, give an example, and if not, explain why this is not possible.
Solution: I can't think of any example or disprove the...
7)
T:R^{2}->R^{2} projection transformation on X-axes parallel to the
line
y=-\sqrt{3}x
find the representative matrices of T{*} by B=\{(1,0),(0,1)\} basis
how i tried:
i understood that the x axes stayed the same but the y axes turned
into
y=-\sqrt{3}x
our T takes some vector and...
Homework Statement
*see attachment for diagram*
I'm having trouble understanding a step in an example problem.
"The Z-axis is vertical and carries the unit vector
\vec{K}=\vec{j}cos(\gamma)+\vec{k}sin(\gamma) "
is what I cannot understand.
The Attempt at a Solution
I want...
Hello,
Just wondered what the correct way is to display physical units on chart axes.
Let's say for example thermal resistance of a heatsink extrusion is plotted as a function of length, and so the units for the y-axis are K.W-1
My 'A' Level physics teacher always insisted on (in order...
I was reading through my textbook and it said that the angle between the axes of two inertial frames, one stationary and one moving at velocity v is supposed to be tan^-1(v/c). I assumed this would be easy to show, but after spending a couple of hours on this probably trivial problem, I can't...
Dear Fellows,
I am plotting in matlab, and defined and axis along horizontal in such a way
x=0:0.2:1.2;
for
plot (x, u,'re--' )
but I need to define the limitation of u along vertical axis,,,,
can anyone suggest me the exact for range -5 to +1
Regards
Dear Fellows
I am working on Mathematica and found my graph successfully but the problem only I am having is how to label my graph,
command of my plot is
Plot [Re[u], {x, 0, 1}, Frame -> True]
which shows the range of x-axis but I also want to define range of my y-axis ,,,
can...
Hi all, I consider a square planar molecule such as XeF4, Xe atom is at the center, F atoms are at the corners of a square. In the character table of D4h group that XeF4 belongs to, I see that there are two C4 axes but I only can find one that goes through the Xe atom and is perpendicular to the...
Hi, having trouble determining the convention for determining the orientation of the principal axes.
(Please refer to the attached file for a diagram of my question)
So in Q1, theta = -19 degrees and the principal axes is rotated one of the following the conventions (from what I can tell)...
According to the character table for the C3v point group there are 2 C3 rotation axes along the z axis. How are there 2 of them? There is only 1 listed in the C2v point group table which makes sense but I can't see how a molecule like NH3 has more than one rotation axis along the z axis.
Hi,
I have just started working with mathematica and I am making a few manipulable plots of differential equations. The problem is that when I use the slider to change the value of certain parameters, the size of both axes change along, which makes it difficult to compare graphs.
I would...
Homework Statement
4) In the above figure, the horizontal axis is x measures in meters, the vertical axis is t measured in meters (SR units!)
a) For the pairs of events AB, AC, CB, determine the metric distance between them.
b) For each pair answer whether the first member of the pair...
I have a m*n matrix of values called plot_1. The matrix contains a series of values intended to be plotted at specified (x,y) coordinates. I am trying to plot the matrix using the surf function.
My problem is that the plot comes up with the axes corresponding to the indexing location (row...
Hi,
can anyone kindly explain to me (assuming no knowledge of spectral theorem, but only simple linear algebra understanding) how to see the vanishing of the terms Ixy, Iyz etc., where only the terms Ixx, Iyy and Izz remain?
Thanks.
Homework Statement
Two speakers at (x,y,z)=-L,0,0 and (x,y,z)=(0,-L,0)
Find the amplitude at all positions in the plane x=y
Homework Equations
The waves are given by:
\tilde{f}_x(\overline{r},t)=\frac{A}{r_x} e^{i(kr_x-\omega t)}
\tilde{f}_y(\overline{r},t)=\frac{A}{r_y}...
Having trouble with this "Moments about the coordinate axes" problem!
When a force F is applied to the handle of the valve shown, its moments about the x and z axes are, respectively, M_x= -77 lb ft and M_z= -81 lb ft. For d=27 in., determine the moment M_y of F about the y axis...
Homework Statement
x^{2}-4xy+y^{2} - 1= 0
Homework Equations
Rotation of axes equations:
x = X cos(\alpha)-Ysin(\alpha)
y = Xsin(\alpha) + Ycos(\alpha)
Alpha is given in the text as:
cot(2\alpha) = \frac {A-C}{B}
but I used the fact that:
cot(\alpha) = \frac {1}{tan(\alpha)}...
i have 3D plot in matlab
lets say i use example isosurface from MATLAB help
[x,y,z,v] = flow;
p = patch(isosurface(x,y,z,v,-3));
isonormals(x,y,z,v,p)
set(p,'FaceColor','red','EdgeColor','none');
daspect([1 1 1])
view(3); axis tight
camlight
lighting gouraud...
Centripetal accelerations with two parallel axes -- the "Scrambler"
Homework Statement
This should be a pretty quick and straightforward question to answer. The problem regards centripetal forces on an object rotating simultaneously around two parallel axes, like in the "Scrambler" amusement...
It is a known fact that every rigid body has a set of orthogonal axes called principle axes about which when rotated the angular momentum vector and the angular velocity vector point in the same direction. Inside the body we can take any point as the origin and find a combination such that the...
Hi
I´m self-studying Alonso and Finn´s Mechanics and I have a question about this subject.
Let a body rotate about an arbitrary axis P having angular momentum \vec L .
Consider a referential with three perpendicular axes, X_{0} , Y_{0} , Z_{0} , which are also principal axes of...
I'm having trouble finding information online regarding figuring out vector components when you set up your own axes. All examples just show a basic x-y coordinate system where the cos and sin components of the vector are obvious.
However, suppose you have a problem where, for example you have...
Hi there,
Making a nice visual for a quantum problem, which is finding the probability of finding the object outside of the classically allowed region for n=0,1,2. One problem: How do I make the y-axis stop after the origin so it doesn't mess up my arrows or my text (see attached)?
Any...
sqrt(1/2)up = sqrt(1/2)right + sqrt(1/2)left
this is very counter intuitive for me, I am used to normal Cartesian coordinates where u can add and subtract magnitudes in the x-axis all day and get nothing on any other axis. furthermore, a spin to the right should be the opposite of a spin to...
Hi,
it is a clear fact that rotations in 3D keep the vectors on the rotation axis unchanged.
In 2D only the zero vector is unchanged.
How can one generalize the concept of rotation axis in N-dimensions?
I've read that for example in 4D one can only rotate around planes.
So are the...
Let me start by saying thank you to any responses I receive. I understand the methods for solving this problem but I have concluded that either part or all of my solution is incorrect.
After solving for the angular velocity, I differentiated my answer in order to check the angular...
Hello,
I have been trying to make a parametric plot with logarithmic axes in Mathematica, but have been unable to find an option to do this. Can someone tell me how to do this? My code is below, and for reference, EnergyScint[b] is the Bethe-Bloch equation for energy deposit for a fully...