All Questions
Tagged with classical-mechanics reference-frames
30
questions
17
votes
2
answers
7k
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Lagrangian of an effective potential
If there is a system, described by an Lagrangian $\mathcal{L}$ of the form
$$\mathcal{L} = T-V = \frac{m}{2}\left(\dot{r}^2+r^2\dot{\phi}^2\right) + \frac{k}{r},\tag{1}$$
where $T$ is the kinetic ...
- 377
10
votes
2
answers
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How can you solve this "paradox"? Central potential
A mass of point performs an effectively 1-dimensional motion in the radial coordinate. If we use the conservation of angular momentum, the centrifugal potential should be added to the original one.
...
- 521
3
votes
2
answers
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Why does a body not rotate if force is applied on the centre of mass?
The definition of centre of mass on Wikipedia is given as
This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration.
How can I prove that such ...
- 517
22
votes
1
answer
5k
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Bernoulli's equation and reference frames
So I was thinking about this while driving home the other day.
I've never been quite clear on why when you drive with the windows down air rushes into your car. I thought this might be explained by ...
- 381
15
votes
3
answers
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Do we need inertial frames in Lagrangian mechanics?
Do Euler-Lagrange equations hold only for inertial systems? If yes, where is the point in the variational derivation from Hamilton's principle where we made that restriction?
My question arose because ...
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7
votes
2
answers
5k
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Centrifugal Force and Polar Coordinates
In Classical Mechanics, both Goldstein and Taylor (authors of different books with the same title) talk about the centrifugal force term when solving the Euler-Lagrange equation for the two body ...
- 115
4
votes
2
answers
599
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Work done changes between reference frames?
(This is not homework; a friend shared with me this puzzler and neither of us can figure it out.) Suppose you are in a plane traveling at velocity $v_1$ relative to the ground. The flight attendent ...
- 43
1
vote
1
answer
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How can I interpret or mathematically formalize Maxwellian, Leibnizian, and Machian space-times?
I've been reading the book, World Enough and Space-Time, and I came across a rough list of classical space-times with varying structural significance.
Here is the same list, minus Machian Space-time,...
18
votes
6
answers
9k
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How can the centripetal force lead to objects flying apart?
I don't understand how the centripetal force, which always points to the center of our circular motion can cause this scenario:
We have a big stone which spins very fast, so fast that a part breaks ...
- 396
8
votes
9
answers
2k
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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:
$$ \mathbf{\dot{L}}+\mathbf{\omega} \times \mathbf{L} = \mathbf{\Gamma},$$
...
- 1,038
2
votes
2
answers
4k
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During a collision, why is momentum not conserved in a participant's frame of reference?
[This question is inspired by an astute observation from a student of mine.]
When we discuss conservation of momentum, students often ask, "When is momentum conserved?" And the lazy, mechanical ...
- 4,841
10
votes
3
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Lagrangian equations of motion for ball rolling on turntable
The equations governing the motion of a ball of mass $m$, radius $R$ rolling on a table rotating at constant angular velocity $ \Omega $ which are derived using Newton's laws are: (I present these for ...
- 145
9
votes
2
answers
5k
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How do I transform onto a relativistic rotating frame of reference?
In classical mechanics, the usual formula to translate the evolution of a quantity as seen from an inertial frame of reference to a rotational frame is: $$\frac{d \textbf{A} }{dt} \vert_{Inertial} = \...
- 24.9k
8
votes
3
answers
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Apparent violation of the law of conservation of angular momentum in the torques experienced by two interacting electric dipoles
Question
Consider two dipoles $({p_1}\hat{i}$ and ${-p_2}\hat{j})$ kept in the $x-y$ plane at $(0,0)$ and $(d,0)$ respectively. Calculate the torque about the COM.
Approach 1
Suppose we select the COM ...
- 1,295
8
votes
3
answers
741
views
In a general physical sense, is the position of a particle really a vector?
Is it consistent to define the position of a particle in some frame as a vector or is just an informal representation? Velocity and acceleration can be added up and multiplied by real numbers and ...
- 1,290
6
votes
6
answers
691
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Validity of rotational Newton's second law in a changing instantaneously inertial frame
A standard textbook question is to ask about some rigid body (say, a 2D disk) rolling down an incline without slipping (cf. John Taylor's Classical Mechanics, Problem 3.35).
The standard approach is ...
- 1,095
6
votes
1
answer
603
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Energy usage in different reference frames
Imagine a moving object at constant speed (like a car). This object is, then, accelerated for a brief moment. In different reference frames (at rest and moving along with the object), the variation of ...
- 133
4
votes
1
answer
392
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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 ...
- 909
3
votes
4
answers
675
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Understanding the definition of tangent basis
This question could sound silly but I though a lot about it and I'm not new to physics.
Let's say I have a plane on which I use polar coordinates, it means a point $P$ can be indicated by its ...
- 1,904
3
votes
1
answer
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Why is total kinetic energy always equal to the sum of rotational and translational kinetic energies?
My derivation is as follows.
The total KE, $T_r$ for a rigid object purely rotating about an axis with angular velocity $\bf{ω}$ and with the $i$th particle rotating with velocity $ \textbf{v}_{(rot)...
user86425
2
votes
3
answers
2k
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Lagrange Equations for Non-Inertial Frame of Reference
I am trying to expand my limited knowledge of Lagrange's equations for evaluating motion. Regarding the Lagrangian in a rotating coordinate system, the text Mechanics by Symon states "...we use ...
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2
votes
1
answer
171
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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 ...
- 980
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votes
2
answers
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When does not Newton's 3rd law apply?
Is Newton's 3rd law valid in non-inertial frames?
If so, then are there other cases for which Newton's 3rd law is not applicable?
- 17.1k
2
votes
2
answers
589
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Galilean transformations of velocity
If I perform a Galilean boost $$x' = x - vt \\ t'=t$$ between two frames $S$ and $S'$, observers in each frame would disagree on the velocity of a particle because
$$ \frac{dx'}{dt'} = \frac{dx}{dt} -...
- 3,986
1
vote
2
answers
150
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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
1
vote
0
answers
3k
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Meaning of centrifugal term in the mechanical energy of a orbiting planet [duplicate]
For a planet under the effect of gravitational force the mechanical energy can be written as
$$E=\frac{1}{2}\mu {\dot{r}}^2+\frac{L^2}{2\mu r^2}-\gamma \frac{m M}{r^2} \tag{1}$$
Where $\mu$ is the ...
- 2,617
1
vote
2
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556
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What does the Problem 14 from Goldstein's book on classical mechanics chapter-7 (special relativity) really mean?
I am having difficulty in understanding problem number 14 in Goldstein's Classical Mechanics, 3rd edition, chapter 7 on special relativity. Here is the problem ---
A rocket of length $l_0$ in its ...
- 1,088
1
vote
2
answers
1k
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Is acceleration frame dependent or absolute? [closed]
as relative acceleration changes from different point of views so property of things in frame should also change but stationary charge do not radiate E.M waves as seen from accelerating frame i.e. ...
- 177
0
votes
2
answers
189
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Rotation of non-rigid bodies-centrifugal effect
Suppose that we have a bar of finite length which is rotating about its center of mass at a constant angular velocity in a horizontal plane. Gravity is neglected.
The fact that the bar stretches ...
- 192
0
votes
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 ...
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