Rotating Definition and 1000 Threads

Homework Statement I want to derive the centrifugal and Coriolis forces with the Lagrangian for rotating space. The speed of an object for an outside observer is dr/dt + w x r, where r are the moving coordinates. So m/2(dr/dt + w x r)^2 is the Lagrangian. The Attempt at a Solution...

Homework Statement Consider an object consisting of two balls connected by a spring, whose stiffness is 400N/m. The object has been thrown through the air and is rotating and vibrating as it moves. At a particular instant the spring is stretched 0.3m, and the two balls at the ends of the...

Hello everyone, I have a quick concept question for electrodynamics course. If a cylindrical magnet, axially magnetized, is rotated round its own central axis, axis of symmetry, will this create a rotating magnetic field in the vicinity of the magnet? what if the magnet was rotated around in...

Homework Statement Homework Equations I=mr^{2} L=ωI ω=\frac{L}{I} The Attempt at a Solution I thought that since the moment of inertia was larger for the ball on the outside its angular speed would be slower. So then it would take longer to hit the wall.

A cylindrical space station of radius r with thin walls and mass M rotates at angular velocity ω such that the apparent gravity on the inner surface of the cylinder is equal to g. 1) Radial spokes of negligible mass connect the cylinder to the centre of motion. An astronaut of mass m climbs a...

Hi, Please could someone explain how they think an accelerometer would work if positioned within the center of a freely rotating sphere (e.g a kicked football)? If using triple axis accelerometer and the ball was kicked from a standstill but with no spin, I would imagine that the...

Homework Statement an ball of mass m is connected by a string with spring constant k, to a rotating shaft. Find a relation between the radius of the circle, and the angular frequency. Homework Equations The Attempt at a Solution Let: Natural length of spring = x0...

[SOLVED] Rotating Square Loop in Constant B-field Homework Statement Homework Equations \epsilon = - \frac{d\Phi}{dt} \Phi = BAcos(\theta) = BAcos(\omegat) d\Phi = -BA\omegasin(\omegat) The Attempt at a Solution I'm trying to study for an exam and I've got this practice...

Hi, I have a couple of questions about velocities in inertial and rotating frames of reference, related by the following equation: \mathbf{v_i} \ \stackrel{\mathrm{def}}{=}\ \frac{d\mathbf{r}}{dt} = \left( \frac{d\mathbf{r}}{dt} \right)_{\mathrm{r}} + \boldsymbol\Omega \times...

I attached a problem from a practice exam. I'm stuck on part b). Part A, I'm assuming the answer is the standard equation for an infinite current sheet. How do I find induced current? I can only think of using Emf = NBA*ωsintωt Where Emf= I/R, but I don't have resistance. Only other equation I...

Homework Statement A person is on a horizontal rotating platform at a distance of 4.3 m from its centre. This preson experiences a centripetal acceleration of 56m/s^2. What is the centripetal acceleration is experienced by another person who is at a distance of 2.5 m from the centre of the...

Homework Statement Consider the steady flow between two long cylinders of radii R_1 and R_2, R_1 > R_1, rotating about their axes with angular velocities \Omega_1, \Omega_2. Look for a solution of the form, where \hat{\boldsymbol{\phi}} is a unit vector along the azimuthal direction...

Homework Statement The curve x=y^(2) and the line x=4 is rotated about the x axis. Homework Equations pi* integral from a to b of Radius^(2) The Attempt at a Solution pi* integral from 0 to 4 of (square root of x)^(2) dx. My teacher has this answer as 8pi but I think that that...

I’m a woodworker, a math idiot, my trig hasn’t improved since I flunked it 40 years ago and I need help making a Christmas toy for my grand-kids. The values that follow are arbitrary, were extracted using eng graphics software and should be solid. Problem: I have one 2D surface (that...

Homework Statement y=x^(3) +1, x=1, y=1; rotated about x=-1 Homework Equations Washer Method. Pi * Integral from a to b of [Outer radius]^2-[inner radius]^2 The Attempt at a Solution I understand the shell method version but I wanted to learn the washer way for this one. Pi*...

Homework Statement Find the volumes of the solids revolution obtained by rotating the region about the x-axis and the y-axis. y=2x-x^2, y=0 The Attempt at a Solution I know how to get the volume of a function that is rotating around one axis, but the "y=0" is confusing me. Because...

If we have a "quasi-rigid" rotating convective cell where the gas overall rotates at the same angular velocity, we could establish a non-inertial frame of reference co-rotating with this convective cell such that the particles of the gas (seen from that frame of reference) may follow a...

Hi, I am new in comsol. I currently doing a simulation on rotating propeller. I need to obtain vibration magnitude of the rotating prop.. can anyone tell me which type of analysis and how i can get the data? I have been working on this and search over the google for past two week didnt...

if KE=1/2mv^2 and you have a circular object rotating, with it's mass uniformly distributed through the object (ie each part of the disc weighs the same) then obviously certain parts of the disc will be moving faster than others. therefore closer to the middle of the disc, you have more KE...

Homework Statement A uniform disk turns at 3.7 rev/s around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk . They then both turn around the spindle with their centers superposed. What...

Does anyone know the theory behind rotational stability of a (long, thin) axle? I would like to know the maximum allowable rotational speed of a 5 meter long axle. I suppose its something in line with the theory of column stability, but I can't find anything about it. I have made a FEM...

Homework Statement A solid sphere of radius a rotates with angular velocity ω\hat{z} relative to an inertial frame K in which the sphere's center is at rest. In a frame K' located at the surface of the sphere, there is no electric field, and the magnetic field is a dipole field with M=M\hat{z}...

Homework Statement A cylinder rotating uniformly about the x' axis of S' will seem twisted when observed instantaneously in S, where it not only rotates but also travels forward. If the angular speed of the cylinder in S' is ω, prove that in S the twist per unit length is yωv/c(squared)...

Hypothetically, if you had an object on top of a disc on Earth that was rotating clockwise incredibly quickly such that the object had a tangential velocity of almost c, and this disc sat on another disc rotating anticlockwise with the same angular velocity, would the object feel the effects of...

Hi, I want to rotate vectors through 120 and they are unit vectors so they lie on a unit spheres. So basically the tails of the vectors are at the origin and given one vector with spherical coordinates (1,θ,∅), how do I obtain the coordinates of the unit vectors that make 120 degrees with the...

Homework Statement The system is made of a disc the center of which is pinned to the origin (so the disc cannot translate), and some weights that can be stuck on the disc to make it tilt (weights do not translate on the disc) (see images attached). There is no friction whatsoever. The only...

The system is made of a disc the center of which is pinned to the origin (so the disc cannot translate), and some weights that can be stuck on the disc to make it tilt (weights do not translate on the disc) (see images attached). There is no friction whatsoever. The only force is gravitational...

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...

Homework Statement Two objects of equal mass are on a turning wheel. Mass 1 is located at the rim of the wheel while mass 2 is located halfway between the rim and the axis of rotation. The wheel is rotating with a non-zero angular acceleration. For each of the following statements select the...

What is the difference between tangential and radial acceleration for a point on a rotating body? As far as I know, the tangential acceleration changes the magnitude of the linear velocity of the point and the radial acceleration changes the direction of its linear velocity. But I don't...

Is there a general rule when to use the shell or washer method when working with calculating volumes of functions rotating about an axis? For instance should I use the shell method when rotating about the y-axis and use the washer method when rotating about the x?

I am writing a science fiction story, and would like some help from the PH community. Details: There is a cylindrical spaceship which is rotating to create artificial gravity. The cylinder has a circular radius of 10km and a length of 30km. The rotational period is 3 minutes and 20...

Homework Statement Consider a rigid sphere of radius 1 and center at (0,0,0) that rotates about its center. The angular velocity is $\omega(t) = (\cos(t) , \sin(t), \sqrt(3))$. Does the path of the point starting at (0,0,1) ever reach this point at a later time? Homework Equations...

Homework Statement Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x, y = 5\sqrt{x} about y = 5 Homework Equations A(x)=∏(R2-r2) The Attempt at a Solution A(x)=∏(5x)2-(5\sqrt{x})2) A(x)=∏(25 x2 -...

Currently my class it calculating volumes of solids by rotating them about some axis, say for instance the function f(x) = x^2 bounded by s = { (x,y) | 0≤x≤1 , 0≤y≤1} and rotating it about the y - axis. I understand the general look of the graph on paper but I can't visualize the actual solid...

Apparently, that's how a lot of car speedometers work... but I don't understand how a rotating magnet inside a coil (or any conductive material, really) can induce a current in the coil. I can understand how pushing a magnet in and out through a coil can induce current, because Flux = Area...

Hi. Ok, so I'm trying to understand the "navigation equations". n: frame traveling on Earth with vehicle. e: frame centered in earth, rotating with it. P: Position of vehicle center of gravity. v^{n}_{P/e} = (vn,ve,vd): velocity of P w.r.t to e-frame, expressed in n-frame. Normally...

"bead sliding on the uniformly rotating frictionless wire in free space" is the standard problem solved in Goldstein's classical mechanics book. The bead moves in outward direction (a=rω2) still why it is called as centripetal acceleration and not centrifugal?

Hello. This has been bothering me. A point mass is on a rotating flywheel that has a constant initial angular velocity, ω0. The object (point mass), initially at some distance r0 from the axis of rotation, now moves out to a further distance rf, and then stops. Say the wheel has a moment of...

Only rotating bodies have angular momentum? Is this statement false? I had read it somewhere that it is false that only rotating bodies have angular momentum, angular momentum = moment of inertia * angular velocity. Both deal with rotation. so how is the above statement false?

Homework Statement I've encountered problems like this: A bullet with velocity v strikes a stick (intially at rest) at a distance d from the center of mass, then the bullet sticks to it, and the bullet-stick system rotates about the center of mass. But they ask me to find weird things like the...

I'm trying to figure this out. Say you have a cylinder of perfectly rotating fluid, so that it's velocity field is: F(x,y,z) = yi - xj which has curl -2k assuming there is 'infinite' fluid drag and you have an 'infinitely' light ball which you place into the fluid at any point (let's say...

It is well-known that associated with the Kerr solution which represents a rotating black hole, there can be a region of space-time where there are loops in space time (non simply connected paths which are navigable in principle). If this is so, it breaks causality and permits time travel in...

Hi folks, I'm an ocean engineer who's getting old and slow. If I have a half-cylinder mass on a shaft where I'd like to be able to quantify energy (which I think I have right) and then have some way of relating that to potential power output. What I have so far: m=18.6 kg Length=0.305m...

Homework Statement A uniform rod of mass M and length L rotates in horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass m are mounted so that they can slide along the rod. Rod rotates with the initial angular speed of ω...

How fast a disk is rotating? Please help me Im trying to attempt this problem, its not a assigned homework problem but it has 2 stars beside it(which means its one of the harder ones) in the book so I am trying to solve it but i don't even know how to begin and have a crack at it. I really...

If a rotating 40 lb. mass has a non rotating 1 lb. mass instantly added to it's central axis, how much will the rotating mass slow down? Secondly, all else equal, does the rotational speed change the proportionality with which the smaller mass slows the larger (inverse square or some such law)?

Homework Statement A proposed space station includes living quarters in a circular ring 62.0 m in diameter. At what angular speed should the ring rotate so the occupants feel that they have the same weight as they do on Earth? The attempt at a solution I assumed that to do this...

Homework Statement mass of the mouse = 0.05 kg disc's radius = 0.2m disc's angular speed = 33 rev / min assume that the angular speed ω doesn't change Homework Equations tangential speed = ω * r The Attempt at a Solution well, what i did was: drew the vectors, one was the...

Homework Statement Hi. I have: A 3 kg bicycle wheel rotating at a 2484 rev/min angular velocity has its shaft supported on one side. When viewing from the left (from the positive x-axes), one sees that the wheel is rotating in a clockwise manner. The distance from the center of the wheel to...