All Questions
Tagged with classical-mechanics reference-frames
204
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Justifying that the gold nucleus is at rest in a Rutherford experiment
This is an example on the Rutherford Experiment from Young and Freedman's University Physics.
In the last paragraph of the solution the book states that it is valid to assume that the gold nucleus ...
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1
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Non-inertial frames in quantum mechanics
In classical physics, non-inertial frames necessitate adjustments to Newton's laws due to acceleration and rotation, yet in general relativity, Einstein successfully incorporates such frames. Why does ...
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2
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1
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Possible error in Marion and Thornton's Classical Dynamics of Particles and Systems
I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3
The rotation matrix associated with 1.2a and 1....
CommunityBot
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2
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Properties of the Center of Mass
My students are currently going through the rigid rotor and hydrogen atom unit in their quantum physical chemistry course and I found myself at a loss on how to justify what seems a natural way to ...
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The square of the center of mass [closed]
In the book Classical Mechanics by Goldstein, there is an exercise related to the square of the position of the center of mass of a free particle. I must prove that
$$M^2R^2 = M\sum_i m_ir_i^2 - \...
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2
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Does relative motion allow for speeds $>c$?
If motion is relative, (so if X was stationary and Y was moving at v m/s, we could think of this as Y being stationary and X moving at -v m/s), could we not create a scenario in which a stationary ...
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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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2
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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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2
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Energy in different coordinates in central force motion
With reference to central force, we see that K.E has 2 terms in 2D cartesian cordinate but just 1 term in polar coordinates and potential energy has 1 term in cartesian but 2 terms in polar.
Basically ...
- 6,744
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1
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Doppler shift phenomenon for non-inertia frames
The Doppler shift phenomenon is well understood when the source and observer are in relative constant motion. However, I'm curious to know how the Doppler shift phenomenon is modified when they (i.e., ...
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2d elastic scattering with an impact parameter
Hello guys I have homework that has tasked me with connecting the effect of the scattering parameter to the energy transfer in a 2d elastic collision of two arbitrary spheres with one of them standing ...
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1
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344
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Find COM velocity with respect to laboratory reference frame [closed]
I'm trying to solve the following homework question.
Suppose that in the laboratory frame of reference we have $2$ particles. Particle "$a$" is at rest with total energy $E_a$, while ...
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2
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Why isn't there such a thing as "internal momentum"?
The three most well-known conserved quantities in classical physics are energy, momentum, and angular momentum.
Suppose we have a system with no external forces acting on it. We can talk about the ...
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3
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391
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What is the velocity of centre of mass in centre of mass frame?
Velocity of centre of mass in centre of mass frame is considered zero. But how are the two contradictory statements written in the book?
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How do physicists determine where to place the world or inertial frame when describing the equation of motion of an object?
For example, I have a pendulum as shown in the diagram above. I would like to write down its equation of motion. To do this, I must define a world frame (or inertial frame, or origin).
But this is ...
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Time derivative of a "general" vector $\vec A$ in an accelerating frame: what about e.g. velocity $\vec v$?
According to Morin "Classical Mechanics" (Section 10.1, page 459), the derivative of a general vector $\vec A$ in an accelerating frame may be given as
$$\frac{d\vec A}{dt}=\frac{\delta \vec ...
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4
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Shape of water in rotating bucket
I need to show that the surface of water in a bucket rotating with constant angular velocity will have parabolic shape. I'm quite confused by this problem, but here's what I did:
$$\vec{F}_{cf} + \...
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Why is the centre of mass useful in a discrete particle system?
How does the concept of center of mass apply to discrete particle systems with varying masses and motions, especially when dealing with a large number of particles?
Considering the challenge of ...
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Question about distribution of mass
I recently began taking my first university-level physics course after having studied quite a bit of pure mathematics. While I think that my math background has helped me grasp some concepts a bit ...
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4
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Reference frame doubts about isotropy
Landau & Lifshitz on p.5 in their "Mechanics" book states the following:
...a frame of reference can always be chosen in which space is
homogeneous and isotropic and time is homogeneous....
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How do 4-vectors change under an "accelerated" Lorentz transformation?
I assume that an observer moving with velocity $\mathbf{v} = v\mathbf{n} = \mathbf{v}(t)$ (with respect to another observer) has coordinates
where $x^{\mu}$ are the coordinates for the observer who ...
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Reading on weighing scales at the equator of a moon in a tidally locked two-body system
I'm trying a made-up extension of this problem. Consider the planet Mars and its moon Deimos, which can be approximated as meeting the following simplifying conditions:
Both objects are perfect ...
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2
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Question about velocities in different reference frames
Suppose $\hat{x^{'}}, \hat{y^{'}}, \hat{z^{'}} $ are the unit vectors of an inertial frame and $\hat{x}, \hat{y}, \hat{z} $ are the unit vectors of a frame which maybe accelerating, rotating, whatever....
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Doubt in fictitious forces chapter in Morin
The question is this -
I know 2 is what the non-inertial frame measures, but isn't $\frac{d\mathbf{A}}{dt}$ the real thing, the physical thing? And you can write that too in terms of the unit vectors ...
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Weird sign in EOM: Centripetal vs. centrifugal term [duplicate]
Something goes wrong when I was deriving the equation of motion in Kepler's probelm, as below,
Angular momentum conservation $L = Mr^2\dot{\theta}^2$.
And Lagrangian is $L = \frac{1}{2}M(\dot{r}^2 + ...
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According to inertial frame, how can a bead move in a groove made on a rotating table? [duplicate]
Context:
Consider a smooth circular table rotating uniformly. Along it's radius , a groove is made. While it's rotating , a bead is placed on the groove gently at some distance (say $x$) from centre. ...
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1
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Does work depend on a point of reference? [duplicate]
Imagine there is me, Earth and some other guy. Me and a guy move parallel to each other at the speed of 1000m/s relative to Earth.
I am so fit that my mass is 0.5kg, so when a force of 1N in the ...
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On the isomorphism between directed line segments and "abstract vectors" (Gregory Classical Mechanics)
I have just begun reading Gregory's Classical Mechanics and, amazingly, he has blown my mind in the first chapter discussing nothing more than measly old vector algebra. Fascinating that Gregory was ...
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Solving a two-body problem using relative motion and reduced mass
I'm having a hard time trying to understand fully this topic and how reduced mass and relative velocity should be used. Let's say we have some sort of mechanical problem regarding the interaction (or ...
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3
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How can mechanical energy be preserved if the potential energy is negative? [closed]
If I set the upwards direction as positive, the gravitational acceleration $g$ will be negative (and thus, $mgh$ will be negative if $h$ is positive). Thus, the potential energy will be negative, but ...
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4
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228
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Is angular momentum conserved on a spinning sphere, specifically Earth [closed]
Specifically in relation to meteorology. I was wondering if the angular momentum an object, lets say a parcel of air has due to the roation about the earths axis. Is it conserved if moved to a ...
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3
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466
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Why isn't frame of reference called reference point? [closed]
A frame of reference is the perspective you have on a happenstance. But isn't it a viewpoint or point of view? As in, a literal point, from which something is observed?
If so, why is it called a frame ...
2
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1
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Why is this hamiltonian not the energy? [duplicate]
Let a pendulum of length $\ell$ be connected to a rod that rotates with constant angular velocity $\omega$. $\theta$ is the angle of the pendulum wrt $z$ axis ($z$ axis is parallel to the rod).
I ...
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Why is simultaneity a requirement for the distance function of Galilean space?
At the end of Chapter 2 of his Course in Mathematical Physics, Szekeres discusses the notion of a symmetry group. I present my definition, adapted from his, here:
We say that a transformation $g: X \...
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1
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Having trouble deriving the exact form of the Kinematic Transport Theorem
The Kinematic transport theorem is a very basic theorem relating time derivatives of vectors between a non rotating frame and another one that's rotating with respect to it with a uniform angular ...
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142
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Correct Lagrangian for classical central force problem?
Wikipedia gives the following Lagrangian for central force problem:
$$\mathcal{L}=\frac12 m \dot{\mathbf{r}}^2-V(r)$$
where $m$ is the mass of a smaller body orbiting around a stationary larger body. ...
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3
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Angular momentum of $N$ particles
I am reading Goldstein's Classical Mechanics book; I have difficulty understanding these lines. Why do the last two terms vanish? I am reading this and thinking $r'$ is a null vector, but the second ...
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Is work done relative according to the theory of special relativity?
I performed a thought experiment.
Consider a body $A$ and another body $B$.
Body $B$ is moving at velocity $v$ in direction $x$ with respect to $A$. This implies that body $A$ is moving at velocity $v$...
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5
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Do released objects take the direction and speed of their parent frame's velocity, or just the parent frame's speed component?
Context: I'm working on a space game. I noticed that an unpowered object fired from a strafing spaceship appeared, as the released object moved, to curve in the direction the ship was strafing. This ...
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1
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Center of Mass calculation in configuration of $3$ pennies inscribing equilateral triangle [closed]
I'm working on a problem that is asking me to solve the moment of inertia about the center of mass of a $3$ penny system where the edge of each penny is touching the edge of the others and the ...
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4
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Why is a reference frame moving with constant velocity with respect to an inertial frame also inertial?
We define an inertial frame, as a frame of reference where:
Newton's 1st law holds.
It is then stated that a reference frame moving with constant velocity with respect to an inertial frame is also ...
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160
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Torque Intuition [duplicate]
We are all taught that the torque $\boldsymbol{\tau}$ is given by $\boldsymbol{\tau} = \mathbf{r}\times\mathbf{F}$ so that torque increases with the lever arm length. What is the physical intuition ...
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Center of mass in hydrogen atom
I have few questions regarding quantum treatment of the hydrogen atom problem.
Why does one changes coordinate from position vector of electron and nucleus to COM coordinates and relative position ...
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How to define differentiation of a time-dependent vectors with respect to a specific reference frame in a coordinate-free manner?
It is usual in classical mechanics to introduce the derivative of a time-dependent vector with respect to a reference frame. This is accomplished through the use of a basis that is fixed with respect ...
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In terms of which zero should i calculate the potential energy in the Lagrangian formalism?
What I understand is that we have two kinds of coordinates when working with the Lagrangian formalism with different zeros (which may happen to coincide) to measure from, those are the Cartesian ...
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9
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Different coordinate system as opposed to different reference frame
I'm having a hard time getting the difference between the two. In Euler's equations of rotating bodies for example, we have:
$$ \mathbf{\dot{L}}+\mathbf{\omega} \times \mathbf{L} = \mathbf{\Gamma},$$
...
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378
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Question regarding d'Alembert's principle
I am new to the subject of Classical Mechanics, I started with Principle of Least Action and now I am learning d'Alembert's Principle. Forgive my ignorance ,but I find it counterintuitive, according ...
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Trajectory of particle thrown from the center of rotating frame of reference
So we have a rotating platform with two frames o reference: the one which is static, $O:\{x,y,z\}$, and the one wich is rotating along the platform, $O':\{x',y',z'\}\ (z\equiv z')$. The platform is ...
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Confusion about imposing constraint in the action
I'm totally confused by one thing. I know that I probably shouldn't be confused about that, but at the moment I don't quite know what fails in the following:
Suppose we have a particle of unit mass ...
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Substituting the conservation of angular momentum into the Binet formula results in contradiction [duplicate]
Background Information
The lagrangian of a particle in a central force field $V(r)$ is
$$
L=\frac12m(\dot r^2+r^2\dot\theta^2+r^2\sin^2\theta\dot\varphi^2)-V(r).
$$
The particle must move in a plane, ...
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