All Questions
Tagged with classical-mechanics reference-frames
204
questions
2
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1
answer
89
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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
$$\frac{d\vec A}{dt}=\frac{\delta \vec ...
- 1,713
15
votes
4
answers
24k
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Shape of water in rotating bucket
I need to show that the surface of water in a bucket rotating with constant angular velocity will have parabolic shape. I'm quite confused by this problem, but here's what I did:
$$\vec{F}_{cf} + \...
- 12.4k
5
votes
5
answers
2k
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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 ...
- 4,231
1
vote
1
answer
62
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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 ...
- 56.5k
1
vote
4
answers
220
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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....
1
vote
0
answers
36
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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 ...
- 207k
0
votes
0
answers
14
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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 ...
- 208
0
votes
2
answers
119
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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....
- 10.6k
0
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1
answer
70
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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 ...
- 147
1
vote
0
answers
38
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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 + ...
- 207k
0
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0
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28
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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. ...
- 341
1
vote
1
answer
52
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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 ...
- 207k
0
votes
1
answer
91
views
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 ...
1
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2
answers
6k
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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 ...
- 207k
-1
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3
answers
121
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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 ...
- 97.9k