Rotating Definition and 1000 Threads

Homework Statement I am trying to answer the following question: Among the animals that appear in the zoo of the Universe there are black holes and neutron stars. The mass of each of these is often the order of the mass of the Sun. The radius of a neutron star is about 10 km and a certain...

I have recently come across the notion that Kerr metric describes the spacetime outside a rotating black hole but not outside a rotating (electrically neutral) star. Unlike Schwarzschild metric, which works both for non-rotating spherically symetric black hole without charge as well as any other...

Hello, I have a few questions about rotation and relative motion. Suppose we transport the proverbial spinning ice skater used to demonstrate conservation of angular momentum to beginning physics students to a universe with only her and two planets. She is now spinning in deep space...

I read that a non rotating planet like Lubricon VI does not have equator because it does not rotate. So why only rotating planets have equator?

how do we know which system of coordinates to use whether (polar) or (tangential and normal) in case of a rotating system ??

Homework Statement A uniform rod of mass M and length L can rotate around point P which is at position x from one end of the rod as shown in the figure. The rod is gently placed on a rough horizontal surface that has a friction coefficient μ. and at t=0 starts rotating with angular velocity...

Homework Statement I'm trying to understand an example from my textbook about angular momentum. This is the example given: For the part in red: I don't understand where the cosine theta term came from. When you're calculating the magnitudes of torques, don't you just use FRsin(theta)? If...

Homework Statement ##M\ddot{y} + k_{eq}y = me\omega^2\sin(\omega t)## What is ##m##? Homework EquationsThe Attempt at a Solution In the ODE above, ##M## is the total mass of the problem, correct? For instance, if we had a cantilever beam, ##M = m_b + m_m(0.23)## where ##m_b## is the mass of...

Hi, I need to transfer electricity to components that are rotating on a shaft but the power source is stationary with respect to the rotating shaft. the electricity is AC. So I had an idea of a rotating capacitor , two round plates , one stationary then a stationary dielectric attached to the...

Consider a solid globe of mass M and of of uniform density. My understanding is that its external gravitational field, in the absence of any other forces, will apply an instantaneous acceleration to any small test mass directly towards the center of the globe. Is that still true in the...

Hi,first time posting here, so please be gentle... I am studying a point mass doing uniform circular motion on a horizontal frictionless table with tension in a string fixed at one end as the center. Everything is clear if center of circle is treated as center of rotation 'O' for the $$\tau = I...

Hi all, I am trying to calculate the torque required by the motor to rotate a disk at a constant speed. Specs are as follows: 1. Disk radius =80mm 2. Disk Thickness =2 mm 3. Disk Weight =50gm 4. Constant speed= 3000rpm(CONSTANT) 5. Motor friction torque= 1mNm 6. Disk position parallel...

Hello folks, I was playing with a rectangular prism 4x4x3 (almost a cube) and I was giving him a rotating movement with the hand over the table so I could see a visual effect I have seen many times in my life and now I remembered to ask about it. So when I give to it an impulse and it start...

So I've been thinking about the Von Braun rotating space station model lately and I was curious about a few things. First, if someone dropped a ball in one (the ship is spinning so the centripetal force is equal to the persons weight on Earth so it creates an artificial acceleration of gravity...

Suppose we have a large circular disk with pegs around the perimeter, and we set the disk rotating so that one pegs passes us every second. Then, we move this disk to a gravitational field, such that one side of the disk is closer to the gravitational mass than the other. From our perspective...

Relative equations: F_net = ma a = F_net/m f = N = _net/I Problem Statement: A spherical bowling ball with mass m = 6.50 kg and radius R = 0.680 m is thrown down the lane with an initial speed of v = 9.00 m/s. The coefficient of kinetic friction between the sliding ball and the ground is μ =...

My first idea is this will result in a elliptic torus. The horizontal semi-axis a=R and the vertical semi-axis b=R*cos(beta). assuming the titled or inclined angle is beta. The distance away from the z-axisis c and it is a constant. But it looks not when I plot the surface in 3D using the...

So I was thinking to myself, if i had a somewhat disproportionate tripodal space structure, how would i make it rotate around a chosen point where the arms of the structure (hallways and passes most likely) converged ? TORQUE AND MOMENT OF INERTIA ! Then I thought about something else...

Homework Statement A 1.60 m long rod rotates about an axis through one end and perpendicular to the rod, with a rotational frequency of 6.91 radians per second. The plane of rotation of the rod is perpendicular to a uniform magnetic field of 0.30 T. Calculate the magnitude of the mf induced...

Hello, I have a Hamiltonian that describes a particle in a rotating cylindrical container at angular frequency ω. In the lab frame the Hamiltonian is time-dependent and takes the form (using cylindrical coordinates) \mathcal H_o=\frac{\vec P^2}{2m}+V(r,\theta-\omega t,z), where V(r,\theta,z)...

Homework Statement A physics student is sitting on a rotating platform. He is holding a heavy weight in each of his outstretched hands. At request of his physics instructor(!) he carries out various manoeuvres to try to change his angular velocity. Which of the following scenarios are described...

Is there a formula for the moment of inertia? A thin, uniform density rod is rotating about an axis that is off the end of the rod, so it looks a bit like this: ------- | (------- is the rod and | is the axis of rotation, so the rod is rotating out of the plane of your screen) I just have...

Bead is at rest on a thin rod pivoted at one end. Bead is about a cm from the pivoted end of the rod. Rod now starts rotating with an uniform angular velocity w rad/sec. 1.What curve does the bead trace from the point of view of an inertial observer? Here what i think... solution of the...

Greetings all, I have been pondering this for a few days and cannot come to a conclusion. Suppose you have Frame-F with basis vectors I, J, & K. Also suppose you have Frame-B (basis vectors i, j, and k) which is rotating w.r.t. Frame-F. In such a case: i = (cos Θ)I + (sin Θ)J j = -(sin Θ)I...

Homework Statement Consider the loop in the figure below. What is the maximum induced emf in each of the following cases if A = 600 cm2, ω = 31.0 rad/s, and B = 0.490 T? Rotating about x,y,z? Homework Equations Faraday's law The Attempt at a Solution This should be relatively easy since the...

Homework Statement Generate a triangle. For this problem, generate a triangle at a grid of points that are finely spaced in the x dimension. The triangle is defined as follows: -Side 1: y = 0 for x = 0 to 2 -Side 2: x = 0 for y = 0 to 1 -Hypotenuse: y = 1-0.5x for x = 0 to 2 Alternatively, the...

Homework Statement A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of...

Homework Statement A metal ring of mass m and radius R is placed on a smooth horizontal table and is set rotating about its own axis with a constant angular speed ω. What is the tension in the ring ?Homework EquationsThe Attempt at a Solution Consider a small element ds=rdθ .Tension T acts at...

Homework Statement Not a homework or coursework question, but given the simplicity of the problem I feel that this is an appropriate subforum. Consider a person spinning a rock on a string above their head at a constant angular velocity, walking away from the observer at a constant linear...

Here's the problem: Two particles of mass $m$ and $M$ undergo uniform circular motion about each other at a separation $R$ under the influence of an attractive force $F$. The angular velocity is $\omega$ radians per second. Show that $$R = \frac{F}{\omega^2} \left( \frac{1}{m} + \frac{1}{M}...

When we release a suspended object, we recover the potential energy due to gravity as the object travels back through the height raised. When we release an extended spring, we recover the potential energy as the object travels back through the distance stretched. But when we release a rotating...

All, I recently completed a project where transient thermal boundary conditions are rotated around a cylinder for a general number of revolutions. In reality, the cylinder rotated but it was much easier to rotate the thermal conditions around the model in the ANSYS environment. I used 360...

Can someone either derive or point me to a derivation of Møller's formula for the relativistic minimum radius of a rotating body? I've been searching for about an hour and it's driving me crazy! The only "minimum radius" equation I've seen imposes the speed limit c on a classical rotating body...

Homework Statement You shine a powerful laser onto to the surface of the Moon from Earth (Earth-Moon distance is 384,000 km or 3.84E8 m). About how fast must the laser pointer rotate (in degrees per second) for the spot on the Moon to move with velocity v>c? Does this violate Special...

Hello all, I have some confusion about rotating. The bad thing is that I don't know where the point is which my confusion starts. As I want to check also my fundamental knowledge about the topic I will ask my questions step by step to see where my problem begins. I hope you don't mind. My...

Homework Statement Consider the inverted pendulum system, where a uniform rigid bar of mass m and length L is elastically hinged on top of a lumped mass M. The bar is constrained by a torsional spring of coefficient kτ and the mass is constrained by a damper of coefficient c. Derive the...

Homework Statement I have gotten the following task: "A smal object is placed in a right circular cone turned "upside-down" with an apex angle equal to 90-2α degrees. The coefficient of friction is big enough to keep the object at rest when it's placed on the inne-side of the cone. After...

Homework Statement A body (let's call it a rod for simplicity) is in frictionless space, and is composed of 4 smaller sub-rods fused (cannot break) end to end. Each sub-rod has a unique mass (m1, m2, m3 and m4) and length (l1, l2, l3, and l4), but they all have the same diameter d. A force...

Homework Statement Coriolis Force - Explain how the following situations would appear in both the inertial and non-inertial reference frames. Assume the inertial frame to be a view from above. Situation 1 - a ball is thrown from the centre of a merry-go-round which is rotating...

I need a contraption that can keep a ball spinning, smoothly, at a slow speed. If it has a variable speed control, that would be better, but minimally it would need to spin a soccer ball and take around 30 seconds to make a full rotation. The look of the device doesn't matter, just that it...

I'm reading Leonard Susskind's The Theoretical Minimum Vol. 1. 1. The problem: I'm on the section in which he asks the readers to derive the Lagrangian for a particle on a rotating carousel in polar coordinates. 2. Relevant ideas: The same Lagrangian in Cartesian coordinates is given as...

Homework Statement We have a disk of mass M and radius R placed on a horizontal plane. A cylindrical groove of radius r is made on a diameter.Now a sphere of mass m and radius r is placed in the groove at the circumference of the disk. At t=0 the whole system is rotated with an angular...

I think this is a textbook-style question, if I am wrong, please redirect me to the forum section where I should have posted this. This is my first time here, so I am sorry if I am messing it up. Homework Statement We have an n-dimensional vector \vec{r} with a constant length \|\vec{r}\|=1...

Homework Statement A rod of length L and made of conducting material is attached with a smaller non-conducting rod of length l to an axle, which is rotating at constant angular velocity ω (see attachment). Find the potential difference between the ends of the rod. Of what strength magnetic...

Hello All, Some background information: I'm a co-op engineering student and recently my supervisor asked me to do a bit of research on a solution to a problem we had. Essentially, a cardan shaft connecting a motor and a gear box failed at a joint during operation and caused some extensive...

This problem came up after drawing a line on the spinning rotor of a food processor. I was idly musing about relativity (parallel motion and perpendicular motion). Maybe some ancient mathematician found the solution while working clay on their potting wheel! Here it is: A flat disk rotates...

Homework Statement Consider the following set of eigenstates of a spin-J particle: |j,j > , ... , |j,m > , ... | j , -j > where \hbar^2 j(j+1) , \hbar m are the eigenvalues of J^2 and Jz, respectively. Is it always possible to rotate these states into each other? i.e. given |j,m> and...

Homework Statement A 45 rpm record in the shape of a solid disk 25 cm in diameter and mass 0.1 kg rotates about a vertical axle through its center. A 15 g spider rides along the edge of the record. Calculate the final angular speed of the record if the spider drops off without exerting a...

Definition/Summary Often in physics we need to consider frames of reference that are non-inertial (the Earth spinning on its axis for example). We must therefore see how these rotating reference frames relate to an inertial reference frame. Equations \frac{d^2\mathbf{r}}{dt^2} =...

Why the Earth is rotating around the sun? I know the centripetal force is required for the rotation of Earth around the sun. But initially there is required some force on Earth to rotate around the sun.