What is Rotating frame: Definition and 42 Discussions
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.)
Hello! I have a radially pointing electric field i.e. at a given radius, R, the electric field has the same magnitude and points radially around that circle of radius R. I have a particle moving around that circle of radius R, with uniform velocity (ignore for now how it gets to move like that)...
From the top of my head, I would say that yes, the very moment our clocks are aligned, and the two bullets are launched it is perfectly ok to use the relativistic velocity addition formula to determine the speed of the bullets from my reference frame. But the more the disk keeps rotating, the...
hi need help in physics HW:
given current density [J][/→]=[J][/0][x][/Λ]
and rotating frame with given surface vector:
$$ A^→ = A_0(cos(wt)x^Λ + sin(wt)y^Λ$$
in need to calculate I(t)
i tried
I = ∫J*dA
but i don't know i to technically do the math
please help me
I solved this in an inertial frame, but now I want to do it in the rotating frame. As far as I can tell the equation of motion is $$\vec{F}_{cent} + \vec{F}_{cor} = mr\omega^2 + 2m\vec{v} \times \vec{\omega} = m\frac{d^2\vec{r}}{dt^2}$$The solutions take a different approach. They state that the...
In my textbook, the effective force of a particle on a rotating frame is given as below:
The diagram is:
What I do not understand is the expression for Rf dotdot, which is given as below:
According to the book, an arbitary vector Q can be expressed as:
So Rdotdot w.r.t fixed frame can be...
Let's say I can see a star in a distance of 1ly in front of me.
I'm sitting on an office chair and begin to rotate with a speed of 1/s (1 rotation per second).
Then I consider me as not rotating and everything else as rotating.
Now I will see the star traveling a circular path with the...
Imagine two frames one inertial (x,y,z) and the other rotating (x',y',z'), their origins are always coincident. The rotating frame is rotating as seen from the inertial frame with a time-dependent angular velocity ##\boldsymbol{\Omega}(t)=(\Omega_x(t),\Omega_y(t),\Omega_z(t))##. In the rotating...
Hi,
I am trying to gain insight into using stationary vs. rotating coordinate frames for natural frequency calculations. I have seen many FE codes suggest that critical frequencies can be calculated differently in rotating and inertial frames, so i wanted to do a 1D calc to see for myself how...
Consider that we have a magnet and a magnetometer (a fluxgate magnetometer with a single coil), standing still as shown in fig 1.
In fig 1, the magnetic field measured at the axis z1 of the magnetometer coil is B1.
But if everything (magnet, magnetometer and the axes) was rotating together...
Hi all,
I was reviewing the Coriolis effect and I came across the attached explanatory image (from the Italian version of a book on physics by Cutnell, Johnson, Young and Stadler).
The idea is the following.
two guys are facing each other on a rotating carousel;
one of the guys on the throws...
Homework Statement
Take the x-axis to be pointing perpendicularly upwards.
Mass ##m_1## slides freely along the x-axis. Mass ##m_2## slides freely along the y-axis. The masses are connected by a spring, with spring constant ##k## and relaxed length ##l_0##. The whole system rotates with...
Hello there,
I have a question (two very similar questions) about the time and phase delay between rotating objects. I want to describe two extreme cases here: I would appreciate any helps.
Case 1
Imagine two observers (people with telescopes maybe) in space that are standing thousands of...
Hello everyone,
I have some conceptual problems understanding the rotating frame transformation.
Take the center of the Earth as inertial frame's origin and another point in Hawaii as rotating frame's origin.
In many lecture notes from internet, or Marion chapter 10.
The vector describing the...
Homework Statement
Let ## \mathbf{r} ## be the position of a point in a rigid body relative to some origin ##O##. Let ##\mathbf{R}## be the position of the centre of mass from that origin. ##\mathbf{r^{*}} = (\mathbf{r}-\mathbf{R})##. ## d\boldsymbol{\phi} ## is the infitesimal vector directed...
Homework Statement
A pendulum of length l at the north pole is moving in a circle to the east at an angle \theta to the vertical. It has some period T_E as measured in the rotating Earth frame. The experiment is then repeated except now the pendulum is moving to the west with period T_W...
I recognize the rate of change of a vector in an inertial frame S can be related to the rate of change of the vector in a rotating frame S0 by the equation below taken from my textbook, where Ω is the angular velocity vector. $$\Big(\frac{dQ}{dt}\Big)_{S_{0}}= \Big(\frac{dQ}{dt}\Big)_{S} +...
Homework Statement
I have a doubt about the way to calculate the centrifugal acceleration for a point P that rotates with angular velocity ##w_1## wtr a inertial frame on a platform that rotates with angular velocity ##w## (##w_1>w)##. I want to find the centrifugal acceleration in the...
Is it meaningful to measure the speed of an object in a rotating frame, and if so how do you do it in the following case? Consider a rim of circumference 100 rotating at 0.8c, both measurements with respect to the inertial lab frame. An object is at a point on the rim with a standard clock...
Hello, I have the following problem:
A system in the lab frame is described by a time dependent rotating potential ##V(\vec{r},t)##.
So ##H_{lab}=\frac{\boldsymbol{p}^{2}}{2m} + V(\vec{r},t)##.
My book says that the Hamiltonian in the rotating frame is given by...
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)...
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} =...
Homework Statement
So this isn't a homework problem but I don't know where else I am supposed to post for general help. I am basically trying to understand the derivation for the equation of motion of a particle in a rotating frame. See attachment for derivation and which steps I am stuck on...
I am sure this is not the best description of the problem, so let me know how I can clarify.
Say there are 2 coordinate systems, with one orbiting around the other. Call one fixed ƒ and the other rotating ρ. The goal is to find the transform between the two frames.
What's known is
1) A...
I'm reading Lanczos: 'The variational Principles of Mechanics'. I need help resolving a paradox - which is probably trivial…
Lanczos (page 100 Dover edition) introduces a system, S', rotating at angular velocity \vec \Omega about an axis through a fixed point with respect to inertial system...
Homework Statement
At t=0 a police officer is located at (0,R) on a circular platform whose radius is R and which rotates around the z axis with constant angular velocity ω. The officer's velocity at that point in time is (ωR ,0). At that time, a bird leaves the center of the platform along the...
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
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...
This is a conceptual problem which I am facing for many days.
If we convert a scenario in an inertial frame into a rotating frame, we apply a pseudo force i.e. centrifugal force radially outwards on the particle. Right?
Also if a particle is having a circular motion in any frame of...
Hi,
I have an equation of the form;
\frac{d}{dt}(W) = \omega \left(x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \right) W + g \frac{\partial}{\partial y} W + k x \frac{\partial^2}{\partial y^2} W
I want to change it into the rotating frame using the transform;
x...
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...
Q 1:Consider a disk of radius R. This disk is rotating around its center with a constarnt angular speed of w. Find the necessary work to move a body of mass m radially with respect to the disk from r=a to r=b.
Q 2:The Bernoulli equation for a unit mass can be written as
gdz+1/2VdV+vdP=0...
Homework Statement
Consider a bead sliding without friction on a circular hoop of wire rotating at constant \Omega, where \phi is the angle between the bottom of the hoop and the bead. Find the equation of motion of the bead.
\hat{\Omega}=\hat{z}
Homework Equations...
i am facing problem in attempting the peoblem attached below
if i work in the non inertial frame (the rotating)
shouldn't the acceleration of m_a after the catch is removed
be simply =\omega2ra
thanks in advance
http://img14.imageshack.us/img14/1399/blahblahr.jpg
Uploaded with ImageShack.us
Homework Statement
These stairs are rotating as a whole while a dog is climbing on them with a velocity v relative to them, as shown.
The angle that these stairs make is 60 degrees, and the radius is R.
1...
Here is the problem: (Question 5-2 in Binney&Tremaine Galactic Dynamics)
Consider a homogeneous self-gravitating fluid of uniform density \rho_0 contained within a rotating cylinder of radius R_0. The cylinder and the fluid rotate at angular speed \Omega about the axis of the cylinder, which...
There is an example in my lectures notes I am having trouble following through:
A particle moving in a rotating frame of angular velocity omega may be described by the Lagrangian:
L= \frac{1}{2} m ( \dot{\vec{r}} + \vec{\omega} \times \vec{r} )^{2}
N.B. \vec{r}.\vec{i} = x , \frac{d \vec{r}...
Homework Statement
At apparent latitude 45◦N a shell is ﬁred due North at an inclination of 45◦
to the horizontal with initial speed V . Show that, neglecting the curvature of the Earth, the shell will hit the ground at a point a distance \frac{2 \omega V^3}{3g' ^2}
East of the line of...
If a coordinate system is rotating, that is time 't' is not independent, then does the acceleration transform as rank 1 tensor?
I thought that it wouldn't because when time is changing, so acceleration will change in a more complicated way than a rank 1 tensor. Perhaps as a rank 2 tensor...
Can someone enlighten me why it is mentioned in the thread
https://www.physicsforums.com/showthread.php?p=769852"
that when the water is viewed from a rotating frame of reference it experiences an outward centrifugal force. This does not make sense to me.
I'm getting confused by this. I have a handout from a lecture that has a derivation that ends with
"\vec{a} = \vec{a'} + 2\vec{\omega} \times \vec{v'} + \vec{\omega} \times (\vec{\omega} \times \vec{r})
Multiplying through by mass, m
m\vec{a} = \vec{F_{ext}} = m\vec{a'} + 2m\vec{\omega}...