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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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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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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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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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 ...
- 367
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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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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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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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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 ...
- 11
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4
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219
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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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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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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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1
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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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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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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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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 ...
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143
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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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141
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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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105
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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 $v$...
user355398
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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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