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30 questions with no upvoted or accepted answers
3 votes
1 answer
47 views

What frame of refernce to select in statistical mechanics?

Suppose we have a solid particle suspended inside a fluid such as an ideal gas, as shown in the following picture: Our system is the solid particle and the environment is the gas (which acts as a ...
Antonios Sarikas's user avatar
3 votes
1 answer
137 views

These components of the angular velocity are given in what reference frame?

When we have a rigid body, the rigidity constraint allows us to write the trajectory $\mathbf{r}_i$ of the $i$-th particle as $$\mathbf{r}_i(t) = R(t)\mathbf{b}_i + \mathbf{w}(t),$$ where we are ...
Gold's user avatar
  • 36.4k
3 votes
0 answers
130 views

Gauge formalism in rigid body mechanics

When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ...
user avatar
2 votes
1 answer
675 views

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....
Elvis's user avatar
  • 43
1 vote
0 answers
36 views

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 ...
K. Pull's user avatar
  • 391
1 vote
1 answer
92 views

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 ...
jvf's user avatar
  • 245
1 vote
0 answers
61 views

Why does my toothbrush topple on rebound?

I noticed this with my toothbrush the other day, but I feel that I have witnessed it happening before. I accidentally knocked my hand into my toothbrush (electric toothbrush, can stand upright on its ...
HelpMe's user avatar
  • 163
1 vote
0 answers
136 views

Assumptions in Galilean and Relativistic Frame Transformation

While deriving the frame transformation equations, either the Galilean Transformation or Lorentz transformation. I have seen almost all authors mentioning/assuming that if an inertial frame $\textbf{S}...
Gaurang Agrawal's user avatar
1 vote
1 answer
83 views

Doubt on the difference between a rotational coordinate system and spherical coordinate system and the calculation of the Christoffel sysmbols

I know basic differential geometry for general Relativity and classical mechanics. But an interesting fact was revealed in my calculations, namely, that I discovered that I didn't realize the ...
M.N.Raia's user avatar
  • 3,085
1 vote
0 answers
90 views

Reference Frame conceptual confusion

I am getting confused as to why a ball still feels gravity when inside a moving car. The point of a reference frame is to reinterpret all the forces acting on a particle in one frame only. Hence all ...
HitchHiker224's user avatar
1 vote
0 answers
403 views

Angular velocities in moving reference frames

Please refer the image below for a clear idea of my question. So, the instructor has written the angular velocity of the wheel, w.r.t. ground and the unit vectors he used are the ones for the frame B....
Sakazuki Akainu's user avatar
1 vote
0 answers
306 views

Rigid Rotor, Heisenberg Picture

I'm running into a problem where a rigid rotor in the the (non-inertial) principle axis frame of reference seems to violate Ehrenfest's theorem by a minus sign. Consider a rigid rotor with ...
Reid Hayes's user avatar
0 votes
0 answers
65 views

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 ...
nomadicmathematician's user avatar
0 votes
0 answers
19 views

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 ...
bobcat's user avatar
  • 1
0 votes
0 answers
14 views

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 ...
Nick_2440's user avatar
  • 208
0 votes
1 answer
44 views

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 ...
Jack's user avatar
  • 959
0 votes
2 answers
61 views

Inertial accelerations like the Coriolis effect are well known. Are there also 'inertial jerks' and what are some examples?

Inertial accelerations like the Coriolis effect are well known. Are there also 'inertial jerks' and what are some examples? My guess would be that it would look something like: $$ j=-3v_r \omega^2 e_r ...
bananenheld's user avatar
  • 2,035
0 votes
2 answers
176 views

Lagrangian of inverted physical pendulum with oscillating base

An inverted physical pendulum is deviated by a small angle $\varphi$ and connected to an oscillating base with oscillation function $a(t)$. The pendulum's mass is $m$ and its center of mass is $l$ ...
herbert123's user avatar
0 votes
1 answer
126 views

Using reduced mass to solve problems

A small block of mass $m$ rests on the bottom of a big box also of mass $m$. If the small block is then given a velocity $V$ to the right, how far has the box moved once the block has come to rest ...
kai's user avatar
  • 67
0 votes
2 answers
521 views

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 ...
Jonathan L.'s user avatar
0 votes
1 answer
115 views

Transport theorem in spacecraft control: tracking a reference angular velocity

I am reading the book named "Analytical mechanics aerospaces systems" by Schaub and Junkins. In section 7.2, the task is to control the spacecraft to track a specified angular velocity $w_r$ ...
sunxd's user avatar
  • 103
0 votes
0 answers
76 views

What is the English phrase for " loi de composition des accélérations" in French. ( Trans. " composition of accelerations law")

I'm looking for details regarding the derivation of a formula called in French" loi de composition des accélérations" ( " composition of accelerations law"). This law allows you ( ...
Floridus Floridi's user avatar
0 votes
1 answer
35 views

Shaped objects positioned in a reference frame

If I have a shaped object (not a point) in a fixed 3-dim reference frame, I believe it takes 6 "pieces of information" to position it: $X, Y, Z$, and three orientation angles. If I add ...
Shookster's user avatar
  • 1,662
0 votes
2 answers
156 views

Generalized coordinates as components

Why we cannot express Generalized coordinates as a vector like we do with Cartesian coordinates $x$ , $y$ ,$z$ ?
Apar Sharma's user avatar
0 votes
1 answer
307 views

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' ...
Edward's user avatar
  • 37
0 votes
0 answers
108 views

Establishing an inertial frame of reference by observing a closed mechanical system?

Suppose one has a closed system of $N$ material points with known masses, $m_1 ,..., m_N$ . Also given are their coordinates as functions of time, ${\bf r}_1(t), ..., {\bf r}_N(t)$, in some laboratory ...
AL1117's user avatar
  • 19
0 votes
0 answers
113 views

Lagrangian of free particle in non-inertial frame

As in Landau & Lifshitz 1st chapter "If an inertial frame К is moving with an infinitesimal velocity e relative to another inertial frame K', then v' = v+e. Since the equations of motion must ...
Ashley Chraya's user avatar
0 votes
0 answers
404 views

Re: Susskind and Hrabovsky: Should the Lagrangian of a particle referred to a rotating frame omit the velocity dependent "potential"?

My question pertains to Lecture 6: Exercise 4 in The Theoretical Minimum by Leonard Susskind and George Hrabovsky. A suggested solution has been posted here: http://www.madscitech.org/tm/slns/ The ...
Steven Thomas Hatton's user avatar
0 votes
1 answer
53 views

"Reference dependence of fuel gauges" in classical mechanics

The power exercised by a force on an object is dependent on the velocity of the object and hence the frame of reference. I am wondering wherein the error lies with arguments such as the ones presented ...
Hmmmm's user avatar
  • 128
-1 votes
1 answer
34 views

Kinetic energy problem for only one existing object

If only a single object were to exist in the universe, what would be the measure of its kinetic energy?I mean what would determine the velocity of the object?I could be one,or could be hunder thousand ...
Suraz Basnet's user avatar