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
3k
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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.
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- 521
3
votes
2
answers
2k
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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
6k
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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 ...
- 12.4k
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
598
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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
419
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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:
$$ \mathbf{\dot{L}}+\mathbf{\omega} \times \mathbf{L} = \mathbf{\Gamma},$$
...
- 1,028
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
answers
3k
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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
331
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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
735
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