Questions tagged [reference-frames]
A reference frame is a particular coordinate system chosen to represent physical entities. The notion is most often used in special and general relativity to denote particular coordinates chosen on the spacetime manifold.
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How does special relativity explain the exchange of things between two observers? [closed]
Consider two observers, O1 and O2, each in their own inertial reference frames, with their frames passing by each other. Each observer has an orange tree, and they exchange oranges as their frames ...
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Does gravitational acceleration vary when changing Galilean reference frames in special/general relativity?
The Lorentz transformations allow us to deduce how the acceleration of a material body changes when we move from one Galilean reference frame to another. But what if we consider not the acceleration ...
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What is the physical meaning of Riemann normal Coordinates?
It's a beginner's question and hopefully not to trivial for this forum: The frame of Riemann normal coordinates (RNC) with regard to a point $P$ in a given metric $g$ is often said to be the reference ...
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Active and passive transformation
Some active transformations on the system can be seen also as passive transformations for example the rotation of the system can be seen as the rotation of the observer in the opposite direction. ...
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Wave hits beach-example: Does sweeping crest constitute a Frame of Reference?
A long wave rolls in at 1 m/s and hits an almost parallel beach.
It's 900k km long, and hits the beach at .1 micro degrees.
Basic math tells us the crest of the wave rides down the beach at a speed of ...
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Newton's first law and Inertial systems
Newton's first law is part definition and part experimental. Isolated bodies move uniformly in inertial systems by virtue of the definition of an inertial system. In contrast, the assertion that ...
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Coordinate transformations in general relativity
Let's assume a non-rotating point mass with mass $M$. A non-massive object travels with constant velocity $\mathbf{v}_t$, with respect to the point mass, in the vicinity of the point mass.
A non-...
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Using Newton's Second Law of Rotation [closed]
According to Newton's Second Law of Rotation
$$\tau_O=I_O\alpha$$
for the torque $\tau_O$ about $O$, the rotational inertia $I_O$ about $O$, and the angular acceleration $\alpha$.
I'm getting confused ...
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Effect of a spring’s mass on acceleration in a mass-spring system
Suppose a mass $M$ is connected to a spring with a spring constant $k$ and mass $m$. Now, assume the system is subjected to a constant acceleration $a$, causing the spring to stretch by a constant ...
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Why do internal torques cancel?
I don't understand why torques produced by internal forces cancel in the sum $\sum \tau$. My textbook gives the following explanation: due to N3L, if a particle exerts a force on another particle of ...
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Meaning of point of application
Work is done when an applied force displaces the point of application in the same direction as the force. I don't understand this definition. The point of application is defined as the point at which ...
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Angular Acceleration of a rigid body about different axes
Angular acceleration of a rigid body about any axis is the same.
Is this statement true? If yes, then why? If not, then what's the mistake in this?
PS:I know there are similar questions already asked ...
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Do hurricanes spin?
It is often said that the spin of a hurricane forms as a result of being in a rotating reference frame with the spin caused by the coriolis force. For example, if you’re on a merry-go-round and you ...
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How the represetation of the motion of a projectile depends on the reference system? [closed]
The question is about the motion (no air drag) of a projectile
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How the represetation of the motion of a projectile depends on the reference system? [closed]
The question is about the motion (no air drag) of a projectile
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Kinematics in moving reference frames
Assume we have an object moving along a path $p_W(t)$ that is described in some fixed reference frame $W$. If we now have a second reference frame $B$ which differs from $W$ by some time varying ...
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Simulate the dynamics of a 3D discrete rigid body from "first principles"
The question stems from wanting to implement a rigid body dynamics simulation without resorting to any of the well-known concepts that are commonly used, such as moment of inertia, torque, and angular ...
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What is wrong with my relativistic explanation of the bucket argument by Newton? [closed]
Newton's bucket argument in my view:
Time dilation is greater at the outer edge of the rotating bucket according to special relativity. This is analogous to gravity in the classical limit. As a result,...
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Is gravitational length contraction only in one direction?
It makes sense to me that an object's length would contract due to gravity. Consider a cube falling towards to the earth. When it lands on the surface, gravity will compress it. This seems to be in ...
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Relativistic kinetic energy in non-inertial frames
This is probably a really silly question, however, I'm having trouble wrapping my head around kinetic energy in SR. For inertial frames of reference, I have absolutely 0 problem in interpreting why $K ...
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It seems the statement "an object in orbit is in a permanent free fall around Earth" is wrong. Is my understanding correct?
Here is an excerpt from an Wikipedia article on low Earth orbit
However, an object in orbit is in a permanent free fall around Earth, because in orbit the gravitational force and the centrifugal ...
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Acceleration in rotating frame
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$\newcommand{\highlight}{\boxed}$
9.5.3 Velocity and Acceleration in a Rotating Coordinate System
Applying Eq. (9.8) to the position vector $\vec{r}$, we have
$$\...
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Why does an accelerated clock record fewer events?
A clock is set up to continuously broadcast its indicated time via radio waves to non accelerating observers in different inertial frames of reference. The clock also continuously records its readings ...
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Covariant and contravariant components or biorthogonal system? [migrated]
For context, these concepts are understood reasonably well. What I am after is a reconciliation between something that is purely geometric in the way of constructive Euclidean projections (with all ...
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Coriolis force relation to wind velocity
I'm learning coriolis effect on Winds moving from equator towards North pole. This is for geography.
Question:
Why is coriolis force stronger for winds having larger speed(larger component of ...
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How to properly change coordinate system using Direction Cosine Matrix?
I am trying to model the behavior of a rocket using Simulink. I use Newton and Euler's laws to compute the accelerations based on the forces and torques on the rocket. I am using two coordinate ...
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Case study on inertia
When our upper body and lower body both are in contact with bus then after applying breaks why only upper body part moves forward?
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Navier-Stokes equations for rotating falling object
I am considering the problem of a rigid body moving in a fluid, free to translate and rotate (say, for example, a falling body in a fluid).
Some of the approaches I found in some articles involve a ...
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Do more distant galaxies move faster with respect to the cosmic background radiation rest frame?
Aparently our galaxy is moving approximately 1/500th lightspeed with respect to cosmic background radiation. While this is certainly fast, it stands to reason that it could had been a lot faster, so ...
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Representing vectors in non-inertial rotating frame of reference
Suppose an object is moving in a circular path about a certain point $O$, with an angular velocity $\omega\hat{k}$ or linear velocity $v\hat{\theta}$. This is basically describing an anticlockwise ...
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If a body in free fall, according to general relativity is weightless, that is, not experiencing force, how does the object gain kinetic energy?
According to the classical Work-Energy theorem, force times distance equals the change in kinetic energy. So, how is it in General Relativity that when a body falls to the ground the body gains ...
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Torque and angular acceleration in rotating frames
If we are using the equation $\tau=I\cdot \alpha$ (where $\tau$ is the torque, $I$ is the moment of inertia, $\alpha$ is the angular acceleration) in a rotating frame of reference, we have to account ...
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Tidal force in equivalence principle
The inertial frame of reference in a gravitational field is defined locally, but couldn't a sufficiently sensitive instrument detect tidal forces in the gravitational field and thus make the frame in ...
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Deriving a formula for average torque on a uniform metal rod with pivot point L from the edge of any side
Okay, this is most likely incorrect since I only have a prerequisite of algebra-based physics and did not take any calculus-based physics yet. I have however taken Calculus 1 and 2 and am quite ...
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Term in double pendulum derivation
I'm working through a particular derivation of the equation of motion of a double pendulum of two points masses m1 and m2 with lengths $l_1$ and $l_2$ using angles off vertical $\theta_1$ and $\...
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Speed of Light Which Varies With Direction in 1+1 Dimensional Spacetime
Suppose there are two frames $(t,x),(t',x')$ in $1+1$ dimensional spacetime, with coinciding origins at $t=t'=0$. Furthermore, suppose that unprimed frame observes the prime frame moving at velocity $...
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Decomposing Lagrangian into CM and relative parts with presence of uniform gravitational field
Most problems concerning two-body motion (using Lagrangian methods) often only consider the motion of two particles subject to no external forces. However, the Lagrangian should be decomposable into ...
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Rotation of rigid bodies about a fixed axis
The concept of rotation of rigid bodies about an axis has confused me for some time now. When we say rigid,3-dimensional body is rotating about an axis with an angular velocity $\Omega$, how do we ...
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Angular velocity in body-fixed frame and space-fixed frame
When we solve for a free symmetric top we find that in body fixed frame, the angular velocity precesses. My confusion is regarding the calculation of omega in body frame. When i am in the body fixed ...
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Derivative of angular velocity in a rotating frame
Taylor Relies on these relations
$v = \omega \times r$
$\frac{d}{dt}Q = \omega \times Q$
To show that
$a = a' + 2 \omega \times v' + \omega \times \omega \times r' + \alpha \times r' ...
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Verifying Center of Mass to Lab frame transformation for Yukawa cross section
I have computed the Yukawa-potential cross section for two spinless particles with mass ration $\lambda \equiv m_P/m_T$; where $m_P$ is the projectile mass and $m_T$ is the target mass. I want to ...
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Coriolis deviation of a projectile fired north from the equator
I'm hoping someone can explain to me where I'm getting confused.
I wish to calculate the horizontal (eastward) deflection of a projectile fired due north from the equator, due to the Coriolis effect.
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How is Coriolis acceleration in polar coordinate, different from Coriolis acceleration due to observation in non-inertial frame of reference?
In Kleppner and Kolenkow's book: An Introduction to Mechanics, on page 34 (pasted below) on the topic titled "Acceleration in Polar coordinates", it has been mentioned that:
"when $r$ ...
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Reference for Reichenbach synchronisation and non-standard special relativity
My professor introduced in the last lesson a new method for clock synchronisation, which he called "Reichenbach synchronisation".
In this new method, two clock A and B synchronise themself with the ...
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Why a free rigid body applied with an external force rotates only about its center of mass and center of mass only translates? [duplicate]
Why a free rigid body at rest or going with constant velocity, when applied with an external force or after the application of an impulsive force, rotates only about its center of mass and the center ...
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Rest frame of perfect fluid
I learned that dust is a collection of particles at rest with repect to each other. Thus the four velocity field $U^\mu$ of dust will be a constant and it is easy to think of what the rest frame of ...
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Why is it not possible to describe general Lorentz Boosts using Hyperbolic Quaternions?
The Lorentz Boosts (for 1+1D) can be described by the Split-Complex Numbers. A Lorentz Boost in the direction of $x$ with the rapidity $\alpha$ for a 1+1D-system can be calculated using
$$q \mapsto e^{...
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Rigid body constraint
While going through the rigid body constraint, I encountered the following statement:
For two rigid bodies to remain in contact, the relative velocity of the contact points on both the bodies along ...
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Foucault pendulum equations of motion
All the sources I see for the equations of motion for the Foucault pendulum start with the small angle approximation. Does anyone know a source or textbook that does the full derivation? ...
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Equation of motion - choosing directions for the coordinate axis
I'm not sure this equation is the right one if we invert the direction of the positive $y$-axis.
Am I right if we assume the positive direction of the $y$-axis downwards, that the correct equation of ...
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