Rotating Definition and 1000 Threads

The angular momentum of the electromagnetic field is defined as, $$ \vec{L_{em}} = \int \vec{l_{em}} d^3r. $$ To solve this for a rotating sphere I must consider the cases where r < R and r > R. When I did this problem I thought that there would be two solutions, one for both cases; however...

Homework Statement Not a homework problem but: I am revising rotating frames of reference right now and I know that: a_{inertial}=(\frac{dv}{dt}_{inertial})_{rot}+(w x v_{inertial}) But I cannot seem to understand what (\frac{dv}{dt}_{inertial})_{rot} means; more so the 'rotational' bit...

Homework Statement Imagine that a circular disc is rotating with a frictionless ball on it( ball is not at center of the disc) If we observe the motion of the ball from the rotating frame of reference, then how can we describe its motion? Homework Equations The Attempt at a...

Why does an object on a rotating disc fly off the disc as the speed of rotation is increased? To accelerate, the object must experience a net force in the direction of acceleration -- in this case, away from the disc, perpendicular to the object's velocity vector. But what is this force...

I got stuck going over the derivation of fictitious forces in rotating frames. see specifically http://en.wikipedia.org/wiki/Rotating_reference_frame#Time_derivatives_in_the_two_frames this page to see the proof I'm talking about (sorry i'd love to be able to explain it by myself but...

Hey guys, I am new to this forum, I have a problem and I can't get my head around it. so basically, I have a gate that rotates in water about a pier located in the middle (the gate is is 20 m length from the middle pier on both sides, so total length is 40 m). how do i calculate the force...

Homework Statement The body is formed of slender rod and rotates about a fixed axis through point O with the indicated angular properties. If ω = 4.6 rad/s and α = 4.4 rad/s2, determine the instantaneous velocity and acceleration of point A. I have attached an image of the question Homework...

Homework Statement Rotating with angular velocity ##ω_0## solid homogeneous cylinder of radius ##r## placed without starting forward speed at the bottom of the inclined plane, forming an angle ##\alpha## with the horizontal plane, and starts to roll in up. Determine the time during which the...

Will a ball placed tightly (radius of ball=width of groove) in a groove(length of grove along radius) on a rotating disk have any motion along the groove. The frictional force is zero.

A question I was doing asked to find the equation describing the surface of water placed in a cylinder rotating about its central axis. The question asserts that in the rotating frame, the water is at rest, and centrifugal force and the gravitational force of a volume element are perpendicular...

I assume that the equation that applies for this problem is M = mg * r. The large gear is rigid while the small gear rotates about the axis which passes through the center of the large gear by rotating a motor. What is the momentum which is required to turn the motor? I'm confused because...

Homework Statement A particle of mass m is free to slide on a thin rod. The rod rotates in a plane about one end at a constant angular velocity w. Show that the motion is given by r=Ae^(-γt)+Be^(γt), where γ is a constant which you must find and A and B are arbitrary constants. Neglect...

Homework Statement A disk rotates with angular velocity w. Two masses, Ma and Mb, slide without friction in a groove passing through the cnter of the disk. They are connected by a light string of length L, and are initially held in position by a catch, with mass Ma at distance Ra from the...

Homework Statement Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y = sec(x), y = 1, x = 1, x = -1 on the x-axis. The Attempt at a Solution This should be ridiculously easy but apparently my answer is wrong?! To calculate the...

Is the energy of a rotating cylindrical spacecraft conserved when a point-like astronaut climbs up a spoke connecting the walls with the center of the cylinder? If so, when I calculate the fractional change in apparent gravity at the walls when the astronaut reaches the middle I get different...

Solving "poisson's equation" slowly rotating spherical shell of mass Homework Statement We have that \partial ^{\alpha}\partial _{\alpha}\bar{\gamma _{0\mu}} = -16\pi T_{0\mu} which is very similar to Poisson's equation if we treat each component of the metric tensor as a scalar field (the...

Homework Statement The hollow tube is pivoted about a horizontal axis through point O and is made to rotate in the vertical plane with a constant counterclockwise angular velocity θ'=3rad/s. If a 0.1-kg-particle is sliding in the tube toward O with a velocity of 1.2 m/s relative to the tube...

Homework Statement Q: A rod of length l rotates with a uniform angular velocity ω about the axis passing through its center and perpendicular to its length. A uniform magnetic field B exists with its direction normal to the plane of rotation. The e.m.f. induced between the center and anyone...

Homework Statement A metal rod (1/sqrt(pi)) m long rotates about one of its ends in a plane perpendicular to magnetic induction of 5*10^-3 T. Calculate the number of revolutions made by the rod if EMF induced between the ends of the rod is 1.5 mV. I have been thinking about this problem for...

Homework Statement An electric generator consists of a rectangular coil of wire rotating about its longitudinal axis which is perpendicular to a magnetic field of B = 1.70 × 10-2 T. The coil measures 13.00 cm by 19.00 cm and 200.00 turns of wire. The ends of the wire are connected to an...

Galileo tried to convince church leaders of the correctness of the Copernican Theory. He had difficulties because the leading thinkers of his day couldn't believe in the rotation of the Earth on its axis. They thought that a spinning Earth would be easily felt and the Earth must be stationary...

Pulsars -- Rotating neutron star produces EM radiation? Hello, If a neutron star is composed of neutrons, which do not carry any electric charge then how it's rotation produces pulsars which are electromagnetic radiation? Thanks.

"Find the area of the surface of the curve obtained by rotating the.." 1. Find the area of the surface obtained by rotating the curve y= 1+5x^2 from x=0 to x=5 about the y-axis. 2. I thought to find surface area, we would need to use this formula: SA= ∫2\pi(f(x))√(1 + (f'(x))2)]dx...

Homework Statement Region: f(x) = 2 sin x on the interval [0, π]. Find the volume of the 3D solid obtained by rotating this region about the dashed line y = −1. Homework Equations Integration of pi∫(2sin(x) + 1)^2 dx The Attempt at a Solution...

I wanted to solve the problem of a cone rotating on its side over a table, around an axis that pass through it's apex, like in the figure. What I want to find is the angular speed ω, the spin of the solid, such that the cone "stands" over it's apex. I don't know how to set the condition...

Homework Statement Find the volume of the solid generated by rotating the region bounded by the x-axis, the curve y=3x^4, and the lines x=1 and x= -1. The axis of rotation is the y-axis. Homework Equations Washers method: V=∏∫ [(R)^2 - (r)^2]dr x = (y/3)^(1/4) The Attempt at a...

Homework Statement The thing that is lying on the disk(Disko), is rotating together with disko. After the rotary frequency of disko grew twice (N X 2), friction(rubbing) Force grew F=6 ( F + 6). You have to understand friction Force module at the original frequency. Homework Equations...

Homework Statement taken directly from Rindler A large disc rotates at uniform angular velocity ω in inertial frame S. Two observers O1 and O2 ride on the disc at radial distances r1 and r2. They carry clocks C1 and C2 they adjust to keep with clocks time with S, i.e., they have been adjusted...

Homework Statement (answer is h * 5 /7) Homework Equations gravitational potential energy = mgh kinetic energy = 1/2 mv2 rotational kinetic energy of sphere = 2/5 mv2 The Attempt at a Solution The gravitation potential energy at the beginning at the top is the same as the kinetic...

1. A pot of 'm' water is rotating about Y axis with w angular velocity...Water is not compressible here... What's the height of the water? 2. Fc=m ω^2 r F=mg m/v=ρ=> 3. I solved the ques for rotation around X axis... Fc =mg From that I found out the h But then I found...

Hi so I am trying to build a rotating platform for a system consisting of two 12in. subs approximately 60 pounds, I would like it to rotate 180 degrees and then back with the flip of a switch if possible. I have absolutely no experience in this what-so-ever and all of the auto places want to...

The next situation is presented 2 big circles (blue ones) are rotating in different directions. The left one is rotating clockwise and the right one rotates counter clockwise. Inside the 2 big circles, 2 small circles (pink ones) are embedded...

Hi, I have a standard cell which I would like to rotate. I would like to rotate it in such a way such that when I define some plane in the unrotated cell [hkl] that this same plane corresponds to the [001] plane in the rotated cell. I essentially want to keep the same unit cell, just rotate the...

Hello, I am first year mechanical engineering student and I am struggling with the concept of moment, rotation and angular velocities, accelerations of rigid bodies. Can someone recommend an article with problems or an excerpt from a book or something similar to help me. It would be great if...

Hi, This question is about a discussion in the two chief world systems, the second day about p 230 in the modern science library edition (around figures 10 and 11). I haven't found the excerpt online so I hope someone has the book. As an objection to a rotating earth, the claim that any...

In Minkowski spactime (Flat), if the coordinate system makes a rotation e.g. around y-axis (centred) , for the metric ds^2, how to make the tertad (flat spacetime) as the coordinate system rotats?

Dear All, Hi I am a teacher and also new to the forum! Can someone guide me what happens if Earth stops rotating suddenly! Thanks. Jayesh.

I've been considering petroleum engineering because of the rotating shift structure of drilling engineer work: such engineers typically work for 1-3 weeks, 12 hours a day, and then are off for an equal amount of time. However, lately I've become concerned about the job security of petroleum...

Hi, Homework Statement A horizontal smooth disk of radius R rotates around its axis with constant speed ω. At t=0 a mass m is thrown at speed v0 (in the lab's frame of reference) towards the center of the disk. I am asked to write down the velocity vector of the mass in the lab's frame of...

Homework Statement Consider a bucket quarter filled with oil. When the bucket is rotating with the angular velocity ω, derive the equation of the surface h(x), where h is measured from the lowest of the surface and x is measured from the rotational axis. Does it change if we replace oil by...

http://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_RotationalDynamicsPivotingRods.xmlin this example, the rod is swinging with one end pivoted. conservation of energy was used in this example. the change in potential energy was converted to kinetic energy, and mechanical...

Homework Statement Homework Equations Frotating = Finertial + Fcor + Fcf The Attempt at a Solution For the inertial field: F = -qv x b -kQq/r2 For the rotating field it would be the same term plus the coriolis and centrifugal forces. The issue I'm having trouble with is this: The v...

Homework Statement A cone of height h and base radius R is free to rotate about a fixed vertical axis. It has a thin groove cut in the surface. The cone is set rotating freely with angular speed ω0 and a small block of mass m is released in the top of the frictionless groove and allowed to...

Homework Statement A massless hoop is suspended horizontally and is free to rotate about a vertical axis through its center with a constant angular velocity (omega). Attached to the edge of the hoop is a simple pendulum that is restricted to oscillate in only the radial direction. find the...

My question is kinda simple but it has been causing me some trouble for a while. In the problem of the pendulum rotating about an axis, why isn't the angle of rotation about the axis a generalized coordinate? The doubt appears when i try to write the hamiltonian for the system and i don't know...

KErotational = (1/2)Iω2 420 = (1/2)Iω2 420 = (1/2)I(402) 420/(402) = (1/2)I 0.2625 = (1/2)I 2(0.2625) = I 0.525 = I 0.53 = I

Homework Statement In the attached image, find angular velocity of the rod and the velocities at points B and C. Homework Equations vB|A=0.3ω The Attempt at a Solution How do I know what angle the absolute velocity makes with the other vectors when put in a triangle? How would the velocity...

Homework Statement panofsky 10.3 Find the torque on a solid conducting cylinder rotating slowly in a uniform magnetic field perpendicular to the axis of the cylinder. The Attempt at a Solution let the radius of cylinder r, and the conductivity is σ, the rotating angular...

Einstein, for his GR theory he made a last important effort to make it valid also for rotating objects. So consider the following thought experiment. There is an observer A standing at the North Pole and another observer B sitting on a platform, turning clockwise once every 24 hours, both with...

Homework Statement A rod of length l swivels around an axis, denoted O in the drawing, located on the floor. The initial position is β=45°. A ball B is left to fall at the same time the rod is left to rotate. Who will arrive, first, to the floor: the ball or the edge A of the rod...