Rotating Definition and 1000 Threads

Homework Statement A straight wire has uniform density and total mass M. The wire is bent to form a closed loop, one section of which is a semi-circle of radius a, and the other section the diameter joining the two ends of the semicircle. The body is free to move about the midpoint O of its...

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 Sketch phasors for two alternating fluxes with a 90 degree phase difference. If the two fluxes are directed at right angles, show that the resultant flux rotates. Homework Equations perhpas N\Phi=BANcosθ although I don't think it's necessary The Attempt at a...

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...

Can one approximate an "ether" frame by analyzing "superimposed" rotating frames? If we assume the axiom that all motion is ultimately curved, however small the curvature, it would appear that for every momentum you are going to have a radial vector associated with the non-zero deflection of...

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...

Ok here is what I did: T=\int \vec{\tau} \cdot d\vec{\theta } = \int\frac{\mathrm{d} \vec{L}}{\mathrm{d} t}\cdot d\vec{\theta } = \int \vec{L}\cdot d\vec{\omega} = \int I_{ij}\vec{\omega}\cdot d\vec{\omega} Where I is the inertia matrix. when I carry that out, I get: T=...

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 particle moves in a rotating reference frame along the x-axis as x(t) = xo eat (xo and a are positive constants). The frame rotates with a time-dependant angular frequency ω(t) about the x-axis. The true physical force is in the x-direction of the rotating frame. Break up...

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...

I'm designing something in which an insert fits into a piece of steel square tubing. The insert is held in place by a set screw threaded in the insert, which is in turn loc-tited into an aluminum "plug" (wider surface area) and is clamped to the inner wall of the square tubing with a hex wrench...

Look at picture for more details... Book says... " A body is free to rotate only about the z-axis. Within the body any particle of mass m can move only in a plane parallel to the xy plane." What would the xy plane look like? I am assuming by "xy plane" this does not mean x and y axis...

Homework Statement The center of a long frictionless rod, pivoted at the origin, is forced to rotate at a constant angular velocity Ω in the horizontal xy-plane. Write down the equation of motion for a bead threaded on the rod, using the coordinates x and y where x is measured along the rod...

Homework Statement Solid cylinder: H=0.14m, R=0.05m. Mass density ∂=900-(900r/0.05), where r is distance from axis of the cylinder. A string of negligible mass and length 0.85m is wound around the cylinder, which is set spinning by a horizontal pull on the string with F=2.5N. The cylinder...

Homework Statement A shaft 2 m long rotates at 1500 revs min–1 between bearings as shown in FIGURE 2. The bearings experience forces of 5 kN and 3 kN acting in the same plane as shown. A single mass is to be used to balance the shaft, so that the reactions are zero. The mass is to be...

Homework Statement Essentially, I am trying to determine the force that must be applied to a rotating disc to that stop that disc from rotating in a certain time period. The disc is rotating at 5800 rpm, the disc has a radius of 5 inches, and a thickness of 0.087 inches. The disk is made...

Hi all, Homework Statement My problem is a pretty basic one, in a exercise a rigid rod of mass M is rotating around a horizontal pivot point i one end. The rod has the length L. I now need to derive the equation of motion using the Lagrangian formalism. My question is: Can i view the...

Is it possible for a piece of cement in a rotating cement mixer to travel at constant speed? If we graph a cement mixer (circle) on the Cartesian plane with a radius of 1, then at (1, 0), there would be a gravity vector pointing down and a normal force pointing towards (0, 0). Are there any...

Homework Statement A computer disk drive is turned on starting from rest and has constant angular acceleration. If it took 0.690s for the drive to make its second complete revolution, how long did it take to make the first complete revolution? What is the angular acceleration?Homework Equations...

Homework Statement An homogeneous rod is fixed to an extremity and is rotating around a vertical axis, doing an angle of theta with the vertical. (in the scheme I made I wrote alpha but it's theta! (θ)) If the length of the rod is L, show that the angular velocity needed to make it turn...

Homework Statement A square loop with sides l is centered on the origin and fixed in the center so it is free to rotate around the x-axis. A magnetic field is changing with time B=B_0(1-exp(-a*t)). I need to find a differential equation to describe the motion of the rotating loop...

I've been thinking about these problems for a long time but I really can't wrap my mind around them. Please share your insights! Consider a circle of radius R/8 internally tangent (inside) a circle of radius R. How many rotations does it take for small circle to return to the same position...

A rigid "H" falls rotating about one of its legs. What's its angular velocity? A rigid body is made of three identical thin rods, each with length L = 0.340 m, fastened together in the form of a letter H, as suggested by the figure here. The body is free to rotate about a horizontal axis that...

I require for a project a rotating stand, much like these... http://www.cokerexpo.co.uk/rotating-display-stand.htm ... Which are used in shops However as you can see they have some preset rotation speeds which have nothing like the accuracy that I will require. I need to control the speed of...

Homework Statement Part c: A pendulum is attached to a 0.15m wooden bar sticked horizontally to a table by a string of 0.12m. If the system is revolved with a revolution speed of 1.5 rev per second, what is the angle θ the pendulum make with respect to the vertical axis? Homework...

Suppose that a conducting bar is rotating with a speed ω, around an axis a distance a from one end, and b from the other. Suppose further that it is immersed in a uniform magnetic field B parallel to the axis of rotation, and that the measured difference of potential between both ends is V. I...