Axis Definition and 895 Threads

I was asked to build an experimental setup for one of my friends and I did it successfully. The setup included two eccentric flywheels, spinning in opposite directions on the shafts of two stepper motors that were facing each other. I 3D printed a pair of identical eccentric flywheels and...

Homework Statement A long insulating cylinder of radius R1 has a cylindrical hole parallel to the axis of the cylinder. The radius of the hole is R2, and the distance from the centre of the cylinder to the centre of the hole is a. There is a uniform fixed charge per unit volume ρ throughout...

Can someone please explain what the parallel axis theorem is?

Hello! I am attempting to do an FFT on a signal e^(jω+nδω)t, where t is constant and for n=0:N-1. This signal starts off at ω when n =0 and then increments in steps of δω until it reaches the final frequency ω+(N-1)δω. Performing an FFT on this signal will put me in the time domain so my...

Homework Statement A homogenous disk with radius R and mass m lies in the xy plane so its center matches the origin O. Point O' is on the z axis at a distance s from point O. Axis y' passes through point O' at an angle \theta with the z axis. Find the moment of inertia around axis y'...

A uniform rod of mass M=5.0 kg and length ℓ=20 cm is pivoted on a frictionless hinge at the end of it. The rod is held horizontally and then released. a) Use the parallel-axis theorem to determine the moment of inertia of the rod about the hinge (ie its end). b) Determine the angular...

Homework Statement The matrix A transforms space by rotating counterclockwise around z axis by ∏/4. -What is A? -Find a unit vector s.t. Au=u (make sure the first nonzero is positive) -for what λ's does Au = λu? write answer as a set {a,b,...} Homework Equations Unit vector u =...

Hello! I have data of a damped oscillation (the movement on Y as it dies down in time). Imagine for example a ball that is hanging from a spring and it keeps bouncing up and down under the spring until it stops. The problem is I do not know how to find the axis around which the oscillation...

Homework Statement I'll provide picture for clearer understanding. The solid cylinder of mass ##m## and radius ##r## revolves about its geometric axis at an angular rate ##p## rad/s. Simultaneously, the bracket and shaft revolve about x-axis at the rate ##\omega## rad/s. Determine the angular...

Hi. I understand how to solve surface Area using integration when it is to be revolved about the x or y axis. But when the axis is not x or y I have a difficult time solving it. Please help me. Here is the equation sqrt(x+1) rotated at x=-1 and y=5. the bounds are 1 to 5. since y=sqrt(x+1)...

Homework Statement I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, that's all I need help with. Progress Since the rod is...

Homework Statement Consider a cuboid of lengths a, b and c along the x, y and z axes respectively, centred at the origin. The task is to show that the moment of inertia of the cuboid of mass M and mass density ρ about an axis along the body diagonal, from (-a/2, -b/2, -c/2) to (a/2...

This problem involves torque, and levers. I am so stuck on this, I really have no idea where to even begin. The problem states: "Tom weighs 150lb and he wants to lift a 600lb stone lid form a well. We give him a 12ft, unbreakable lever that has one end attached to the stone (at the COM), and...

Homework Statement A horizontal 845.0 N merry-go-round with a radius of 4.3 m is started from rest by a constant horizontal force of 74.0 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry-go-round after 2.2 s. Assume it is a solid cylinder. The...

I have 2 curves and I need to slide 1 of the circles along an axis until it exactly meets the other circle. How do I determine the distance until contact?

Homework Statement got a vector F (105,300,140) magnitude: 347.3 it wants the angles, 3 of them with the axis x y z Homework Equations all my calculations has lead to the wrong answer, but the correct answer is (180-myanswer) why is that? The Attempt at a Solution...

Homework Statement The equation ax^2 + 2hxy+by^2=1 represents the equation of ellipse if h^2-ab<0. When x=Xcosθ-Ysiinθ and y=Xsinθ+Ycosθ, the above equation transforms to \dfrac{X^2}{\alpha^2} + \dfrac{Y^2}{\beta ^2} = 1 where σ and β are real numbers. Then find the product of major and minor...

Homework Statement A 2.72kg ball is attached to a .65m rod that weighs 1.24kg. The rod rotates around it's axis 125 degrees. After rotating 125 degrees the ball is let go from the rod. How much torque is required to make the ball's exiting velocity 18m/s. Homework Equations t=F*d vf=vi...

Here is the question: I have posted a link there to this thread so the OP can view my work.

This is NOT a HW question. I'd appreciate an explanation of the following: I would like to determine the forces acting on a mass set between two springs of constant k on a slope (the slope's angle is alpha). The slope revolves around the vertical axis with angular velocity w and the mass could...

Need someone to verify that my work is correct please. Consider the region bounded by $y = sin(x)$ and the x - axis from $ x = 0$ to $x = \pi$ a) Find the volume if the region is rotated about the x - axis. $$V = \int \pi (sin(x))^2 \, dx$$ $$ \pi \int^{\pi}_0 sin^2x \, dx$$ $$\pi...

Does a body rotating about an axis also rotate about any other axis? Eg. Cars on a racetrack may be rotating about a vertical axis passing through the centre of the track but can they also be considered to be rotating about a vertical axis passing through the spectators' stand?

http://www.physics.udel.edu/~watson/phys208/exercises/kevan/efield1.html I'm having trouble understanding the derivative notation. I know that "dE" and dQ" have to do with the derivative, but what exactly does that mean in the context of this problem? For some reason I find it difficult to...

As an example of the manipulation of an electron beam, consider an electron traveling away from the origin along the x-axis in the xy plane with initial velocity vi= vii. As it passes through the region x = 0 to x = d, the electron experiences acceleration a = axi + ayj, where ax and ay are...

(Figure is attached) Find the tension in the cable AB such that the net moment about the hinge axis CD induced by the forces F and P is zero. The force F is applied at point A and the force P is applied at point E. The magnitude of the force P is P = 65 lb. Two coordinate direction angles for...

Homework Statement Find the moment of inertia of a hollow sphere about a vertical axis through its center in terms of its mass M and radius R. Homework Equations I=\int r^{2} dm The Attempt at a Solution I've been curious about different methods for finding moments of inertia...

Hi all, I am currently working on a project and have a problem. I am using a 3 axis accelerometer and attempting to measure distance with it. (Yes, I know, the double integration of doom..) My problem is not with the integration so to speak but is just with some compensations. The...

Homework Statement A hydrogen chloride molecule (HCl) has a partial positive charge on the hydrogen atom and a partial negative charge on the chlorine atom. The HCl molecule is placed at A. There will be force on the bromide ion in the +x direction. B. There will be force on...

When one comes across the sentence 'axis of a straight wire', how can one consider the orientation of the axis? Commonly, the axis of a straight wire can be considered to be a line parallel(along the wire) to the wire itself. Can 'axis of a straight wire' also mean a line that is...

Homework Statement This is more of a conceptual doubt. Why does the axis being called as the axis of rotation of a rolling body have to be at rest with respect to some frame of reference? What is the definition of axis of rotation? When is an axis called an axis of rotation?

Hi, It's surprising how little information is available on this topic, considering it seems like such a fundamental problem. The only tutorial I have found is http://www.umich.edu/~ners312/Course%20Library/SolidAngleOfADiskOffAxis.pdf, and my university does not have access to the other papers...

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...

I was wondering if a galaxy could be perfectly orbiting to create a sort of axis of rotation, with a period being like 50 million years, or is it impossible because of some property that elliptical galaxies have? If it is possible, what is the probability that it exists in our observable...

Homework Statement There is the moment of inertia about an x and a y-axis named, I_{x}, I_{y}. Then there is the moment of inertia about the centroidal x and y-axis named, \overline{I}_{x}, \overline{I}_{y}. Often we can look up these values in a table (like the figure included) and apply...

Homework Statement This is moreof a conceptual question regarding the parallel axis theorem and area. Lets say I have a solid rectangle with length L, and Width W. I cut out a circle of radius R at the center. When calculating the Total Area moment of inertia of the hollow region where the...

Homework Statement A constant horizontal force of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.30 m as shown in the figure. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s2. (a) What are the...

I'm trying to find the equation of a general ellipse given 3 points. Two of those points should be at each end of one axis. Using this I have the center of the ellipse, and the angle of rotation with respect to the x-axis that this axis is rotated. It's unknown whether this is the major or minor...

f(-x) is a reflection over the y axis -f(x) is a reflection over the x axis Now, how do we represent a reflection over y=x?

I know that the plane ##z=4-y## is even with respect to the x-axis and is not even with respect to the y-axis and z-axis from graphing the plane. How would I algebraically determine this?

Homework Statement I am doing an assignment where I have this (easy) true/false question. The parallel axis theorem can be used to find moments of inertia of an object about arbitrary axes, provided the moment of inertia about a perpendicular axis through the centroid of the object is...

The outer ring of the wheel has a mass of 51 kg, the inner ring, 6 kg, and each spoke, 10 kg. Find the mass moment of inertia of the wheel about an axis through A and perpendicular to the page. Assume r1 = 124 cm, r2 = 36 cm. Each spoke is 88 cm long. DIAGRAM What I've learned in...

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...