Axis Definition and 928 Threads

I understand internucler axis is a imaginary line about which the molecule rotates.and it's symmetric about the internucler axis. So we can find the internucler axis by symmetry if the moecule is symmetric about some axis. How would we find the internucler axis if the molecule is...

Homework Statement Find the volume of the solid of revolution when we rotate the area limited by the x-axis and the function f(x) = 1 - cosx where x e [0, 2∏] once around the y-axis? The Attempt at a Solution In my notes I have the following equation: V = ∫ 2∏x f(x) dx If I put...

i've seen all the super conductors and how it fixes a magnetic field and then levitates, but on which direction does it fixes? for example: if there was a solenoid pointing upwards(the empty middle is vertical) and moving from the axis of -Y to +Y and a ring of super conductor places higher...

How does it look like if three unit vectors at a point such that each vector is tangent to one of the axes in 3-Dimensional Cartesian System? Can anyone illustrate about this? Thanks.

I'm a mechanical engineer and I am more specialized in structural calculations than dynamic calculations and now I'm faced with a basic dynamic problem and would need some help. I have a solid cylinder (shaft) that I want to rotate around its axis. The cylinder is supported by two bearings at...

relation between r ,ω and θ for rotation around fixed axis. \frac{d\textbf {r}}{dt} = \textbf {ω} \frac{dθ}{dt} = ω \lvert\frac{d\textbf {r}}{dt}\rvert = \frac{dθ}{dt} bold means vector. Is this right?

I'd like to evaluate the integral, \int^{i\infty}_{-i\infty} \frac{e^{iz}}{z^2 + a^2}dz along the imaginary axis. This function has poles at z = \pm ia , with corresponding residues \textrm{res}(\frac{e^{iz}}{z^2 + a^2},\pm ia) = \pm\frac{e^{\mp a}}{2ai} My question is - I'm not sure...

Everybody says that the distance ,between the two axis, used in the formula, is perpendicular. But in the proof it was a hypotenuse. It was not perpendicular.

\(\DeclareMathOperator{\Ima}{Im}\) \(\DeclareMathOperator{\Res}{Res}\) Given \[ \Ima\left[\int_{-\infty}^{\infty}\frac{e^{iz}}{z(\pi^2 - z^2)}dz\right]. \] I know the integral is equal to \[ 2\pi i\sum_{\text{UHP}}\Res(f(z); z_j) + \pi i\sum_{\mathbb{R}\text{ axis}}\Res(f(z); z_k). \] However...

Homework Statement Given that a vector has a magnitude of 6.0 units and makes an angle of 45° and 85° with the x and y axes, respectively, find the x and y components of this vector. Does the given information determine the z component? What can you say about the z component? Homework...

Homework Statement Q is the edge length of the cube. The moment of inertia of the cube about an axis passing through its center and the center of two opposing faces is (1/6)mQ^2 (PCM in the diagram). Use the parallel axis theorem to find the moment of inertia if the axis is along one face of...

I want to prove that: [J_1,G_1] = 0 Where J is the rotation operator and G is the boost operator (subscript refers to the axis). I am using the Jacobi identity: [[J_1,J_2],G_3] = [[G_3,J_2],J_1] +[[J_1,G_3],J_2] Using other identities, I got: [J_3,G_3] = [G_2,J_2] - [G_1,J_1]...

Homework Statement Child P happens to be at a greater distance from the rotation axis than Child M. Which child has the greatest angular velocity? 2. The attempt at a solution Do they have the same angular velocity, and if they do can you please explain. Thank you.

My tutor says Henry Ford opted for a horizontal-bed IC engine for the Model-T as this would avoid having any gyroscopic effects(normally associated with a vertical oriented engine). My question is,how does it matter if the engine cylinders are oriented horizontally or vertically?since the...

Hi there, It's the first time I am using gnuplot to plot a graph and I watched all sorts of tutorials and advices on google but I just can't find a good solution! Let me try to explain what the problem is... The experiment: I have a microphone and a speaker in closed box. The speaker is...

Homework Statement Show that the transformation w = e^{z} + z maps the infinite lines y = \pm\pi into semi-infinite lines u \leq u_{0}, v = \pm\pi. This is equivalent to transforming an infinite or edgeless parallel-plate capacitor (z-plane) into a parallel plate capacitor (w-plane). Sketch...

A planet in another solar system orbits a star with a mass of 4.0 ×1030 kg. At one point in its orbit it is 250×106 km from the star and is moving at 35km/s. Take the universal gravitational constant to be 6.67 × 10−11 m2/s2 · kg and calculate the semimajor axis of the planet’s orbit. The...

Hello MHB, As students of calculus, we are taught to find the volumes of solids of rotation obtained by revolving given regions about horizontal and vertical axes of rotation. But, what if the axis of rotation is neither horizontal nor vertical? Please consider the following diagram: We wish...

Homework Statement Let f(z) = z^{\frac{1}{3}} be the branch of the cube root function defined on \left[0, 2\pi\right). Show that f is not continuous for z_{0} where z_{0} is such that Re(z_{0}) > 0 and Im(z_{0}) = 0. Homework Equations For a sequence of complex numbers, z_{n} = x_{n} + iy_{n}...

Hello, I am having difficulty in understanding how the moment about an arbitrary axis is found as the scalar product of the moment about the origin with the unit vector of the arbitrary axis. Can anyone elucidate this?

How exactly can the angular velocity of a 2 dimensional laminar object be the same with respect to all axes of rotation perpendicular to its plane ?

Homework Statement Compute the area as an integral along the y-axis: f(x) = x^2 - 6, g(x) = 6 - x^3Homework Equations N/AThe Attempt at a Solution I solve for x in terms of y for both equations and end up with: f(y) = +/-√(y+6), g(y) = (6-y)^(1/3) I then look for interception points of the...

Hello everyone! This is probably the stupidest question that I've come up with, and I'm a little embarrassed asking it, but here goes: Is it only the tangential speed that is zero of a point at the axis of rotation in a rotating solid? If not, then I don't understand how the rotational...

Homework Statement Use the method of cylindrical shells to find the volume generated by rotation the region bounded by the given curves about the specified axis. Homework Equations y = x^2, y = 2-x^2; about x = 1 The Attempt at a Solution I tried to just break it down. I want...

I want to model a free 2 axis free gyro. I used to have a very detailed model, but cannot find it. It was cross coupled, and included many disturbance torques. All I am looking for is a great source on this topic. Thanks! Mike

I have always thought of connecting rods as straight and the crankshaft axis being line bored in the same plane as the cylinder axis. Is there an advantage in offsetting the crankshaft slightly to compensate for the difference between the compression and power stroke pressures ? Is the answer...

http://img42.imageshack.us/img42/6336/14vu.png please explain your answer! also if u know of similar problems or where this problem is taken from do tell me coz i have an admission exam coming up soon please explain the following: 1. what is the flux like? 3. how the coil spins? z. how is...

What is quantisation axis? In many books authors just say that we choose that z is quantization axis.

Hi all, Note: The text below is the motivation for my question. To jump to the question immediately, please skip to the line that says HI! I have a set of data points, let's call it A, and I ran principal component analysis to get the top 3 principal components to be able to represent the...

Y=x^2, y=0, x=1 ; about x=2 v=pi r^2 T I tried 0 to 1 intg (x^3-2)^2+2^2 dx, but it wasn't right. Not sure what to do.

Homework Statement Hi there, this isn't a homework question but I need some help with this equation since I'm not the best at mathematics. I would like to rearrange this equation so I can solve for "a" Homework Equations The Attempt at a Solution ?

for a perfectly rigid body, how can one identify what is the axis of rotation of the rigid body? What is the condition required for an axis to be called the axis of rotation?

This is probably a silly question, but I want to make sure I get it right for a story I'm writing. I want to roll an elongated spaceship "around" it's horizontal axis (as opposed to flipping it end over end). Is it equivalent to say "along" the horizontal axis? In this case, I'm assuming...

Hello, I have an image which gets displayed and has the x and y-axis ranging from 0-812 and 0-607 respectively. This is because these are the pixel sizes for my image. I would like to change the x-axis to show -3.85, 3.85 and for the y-axis to show -2.9,2.9. However, when I load my image into...

Hi I am looking at the contours of the following function f, which trace out an ellipse: f(x, y, z) = \exp(-x^2a)\exp(-y^2b) Here a\neq b are both positive, real constants. The axis of these ellipses is along z. Now, I am wondering how to generalize the function f such that the symmetry...

Homework Statement Problem 3.60: Homework Equations M_{AD}= \begin{vmatrix} \lambda_x & \lambda_y & \lambda_z \\ x_{B/A} & y_{B/A} & z_{B/A} \\ F_x & F_y & F_z & \end{vmatrix} The Attempt at a Solution Looking at the figure, these are the unit vector components...

Suppose that two events occur on the x-axis of an inertial frame, Δx apart with a time interval between the events of Δt. a) the proper time interval between the events is...? b) the proper distance between the events is...? I think I'm just getting confused by the wording. I imagined that...

if i have rod of a certain length. let point (a) on one end of the rod and point (b) on the other end. along the rod axially is the X axis, vertically Y axis and Z is the lateral direction.let force prependicular on x -axis at point (b) and move this force to point (a) which will create a...

Homework Statement Homework Equations I=Bmr^2 Parallel axis theorem = Icm + MD^2 WET, KE, PE equations The Attempt at a Solution So far I've only done parts a and b and I wanted to post this up as soon as possible, I want to make sure if I'm on the right path so far. part...

Hi Usually I'm used to dealing with symmetric distributions with mean at 0, but one has come up that cannot take this form because 0 is impossible to attain. Instead, this function seems to have a bell-shaped look, although the mean is around 5 and the tail towards 0 drops off a little bit...

I have a basic question about MEMS gyros - Let's say a dual axis(X & Y) gyro IC is lying flat. Ideally the output reading would be zero. If I lift one end of the IC by some degrees, there would be change in output reading. Let's call this new reading. When the IC is held at this position...

hi. I have an essential question. Suppose we have an complex shape at complete rest freely in space. There exist no forces at all. If we collide it in a point, at which axis it will be rotate? How I find it? I want the answer be in general and for all shapes.

Homework Statement An object is rotated 45 degrees about an axis whose + direction is that of (i-k). Find zxz Euler angles (that is, Euler angles as introduced by Goldstein) for a set of three active rotations that gives the same net motion of the object. Homework Equations...

Homework Statement x^2 + (y - 2)^2 = 1 The hint given by the question was to split the function into 2Homework Equations Surface Area about x axisThe Attempt at a Solution So i did this. (y - 2)^2 = 1 - x^2 y = √(1 - x^2) +2 and y = 2 - √(1 - x^2) The range I calculated when...

I have a question I'm wondering in bode plot we write the horizontal axis w rad/sec what does this mean? is it normal scale 0.1 0.2 0.3 ... etc with equal distances?? it's clear not because it's drwan on semilog paper if it's the horizontal log w why then we write 0.1 ,0.2 ,,1 ...

Hello I have designed a vertical axis wind turbine (Savonius) with a 180deg helical twist. It catches the wind really well but the wind power to electrical power conversion is really poor, it is currently only at 4% efficiency. I think the problem is the dc motor that I am using as a...

I'm a bit confused with this concept of quantisation axis. ##|+\rangle## and ##|-\rangle## spin. And operators ##\hat{S}^+=\hat{S}_x+i\hat{S}_y## and ##\hat{S}^-=\hat{S}_x-i\hat{S}_y## are rising and lowering operator of spin projection. Why z-axis. How is measured that?

Hi i am currently doing my dissertation in which i am designing a vertical axis wind turbine design that is a modification of that of a savonius design. A major problem that i am having is being able to predict the torque value of torque for my design in order for me to then predict the...

Homework Statement https://docs.google.com/viewer?pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxtcnRyYXNrc3BoeXNpY3N8Z3g6NzBjNzQxNzIzNDM4Y2M4MQ&docid=236f6ec6993ab970f48b7263eadc4898%7Ca7825efe08310846ea2fbce00fd8bb0b&a=bi&pagenumber=14&w=791 #39. Homework Equations Ep=KQ1Q2/R The...

in what situations would you require the use of the parallel axis theorem? Also, from the physics book it says that let x and y coordinates of P(a point parallel to the first axis) be a and b. then let dm be a mass element(what does this mean? a point anywhere within the object?) with the...