All Questions
Tagged with classical-mechanics reference-frames
204
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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 ...
- 163
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votes
3
answers
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Why do we consider $L^2/(2mr^2)$ part of effective potential energy?
The energy of a particle under the action of a radial conservative force is given by
$$E = \frac{1}{2}m\left(\frac{dr}{dt}\right)^2+ \frac{L^2}{2mr^2} + U(r),$$
where the last two terms provide the ...
- 799
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Rate of change for vectors between coordinate systems
My question concerns the rate of change for vectors. The rate of change is given by:
$\frac{d\vec{G}}{dt}_{space} = \frac{d\vec{G}}{dt}_{body}+\vec{\omega}\times\vec{G}$.
I'm then asked to derive the ...
- 11
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7
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Why can basis vectors change direction?
I thought that basis vectors were of magnitude one and located at the origin and were each linearly independent, so how in things like polar coordinates can the basis vectors be moving?
- 139
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378
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Question regarding d'Alembert's principle
I am new to the subject of Classical Mechanics, I started with Principle of Least Action and now I am learning d'Alembert's Principle. Forgive my ignorance ,but I find it counterintuitive, according ...
- 367
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58
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Dummy variables and Galilean Invariance
I've faced a small doubt, and I was hoping someone could verify this for me.
According to Galilean transformation, consider $2$ frames - $S_1$ and $S_2$ moving relative to each other. $S_1$ is at rest,...
- 1,791
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1
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Angular velocity across different reference frames
In classical mechanics:
Logically, it appears to me that if I draw a mark on a ball and let it roll, the amount of time that will pass before the mark reaches the same position (in terms of angles: ...
- 183
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6
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690
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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
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2
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250
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Centrifugal Force & Rotating Frames [duplicate]
In Thornton & Marion's Classical Dynamics, the following relation is given for the rate of change of an objects position in the two coordinate systems (according to the picture shown at the bottom)...
- 529
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2
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186
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Resolution of vectors along different directions
I have a small doubt regarding the resolution of forces and vectors.
Suppose, we have our standard cartesian coordinate system, with unit vectors $\hat{i}$ and $\hat{j}$. Now we have defined polar ...
- 1,791
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48
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The E-L equations in a non-inertial frame
These are from pages 126 and pages 127 about the subject, (EDITED: from L&L A course of theoretical physics) but I don't really get one thing.
"Thus an accelerated translational motion of a ...
- 15
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5
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339
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Is "non-inertial" frame a relative term?
I've heard only two definitions of non-inertial frame so far:
I. A frame that is accelerating with respect to an inertial frame.
II. A frame where Newton's Laws are invalid.
Let's begin with ...
- 89
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136
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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}...
- 335
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2
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Acceleration of the center of mass without external forces paradox
From classical physics we know that the acceleration of the center of mass of an object is zero if there is no external forces.
Can someone tell me what's wrong with this counter example:
Counter ...
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answer
131
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Newton's 1st law, applied in a manifold
A seemingly interesting question.
Newton's 1st law states that objects continue in straight lines, unless acted upon by external forces. Now consider a frictionless manifold. Since it is locally ...
- 428
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115
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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 $w_r$ ...
- 103
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Special relativity v.s. "homogeneous time" within an inertial reference frame
I am asking a conceptual question.
As we learned from classical mechanics, say Lagrangian formulation, as stated in Chap 7.9 of Classical Dynamics book by Thornton-Marion (5th Ed) p.260:
in our ...
- 4,336
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1
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Is work done by the internal forces independent of the frame of reference?
This question is about work done being dependent on the frame of reference, which is, obviously the net work done.
I ask what is the reason for the work done by internal forces to be independent of ...
- 362
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3
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335
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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
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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 ( ...
- 373
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332
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Understanding Euler's Rotation equation for rigid bodies (Frames Of Reference)
$$
\tau_b=I_n\dot\omega_b+\omega_b\times I_b\omega_b
$$
Now in the above is Euler's famous rigid body rotation equation, in the body frame of reference ..... this does not make sense to me. How can a ...
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1
answer
494
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Conservation of angular momentum and reference frames
I have read in Physics (Alonso-Finn) that, for a system of particles, the relation
$$ \dot{\vec{L}} = \tau_{ext}$$
holds only if both $\vec{L}$ and $\tau_{ext}$ are calculated w.r.t. to a point which ...
- 1,252
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2
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342
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Why is angular momentum conserved in a central field?
I am trying to understand how a gyroscope works, which in the broad strokes is due to conservation of angular momentum. I understand the case when the angular momentum passes through the origin of ...
- 383
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209
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Will the plane of oscillation of a pendulum change if I rotate the suspension point
I'm having trouble understanding Foucault pendulum and from that I've extracted one of my doubt and here it goes:
A pendulum on a fixed platform is shown
Now if we rotate the platform as shown
Will ...
- 1,270
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54
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A thought experiment to prove that Newtonian gravity is incomplete [duplicate]
A particle is at rest in one frame having mass $m$. It'll attract another mass proportional to its mass ( newtons law) .
We jump into another frame moving close to speed of light. In this frame it's ...
- 1,270
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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 ...
- 9,381
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1
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35
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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 ...
- 1,662
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130
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Problem regarding equations in different frame of reference
Previously I asked this question and got the following answer.
I'm asking for reason why you can split Tension(first case) but not mg(second case)
When you say 'splitting,' you really mean ...
- 195
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427
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Angular velocity to linear velocity Modern Robotics textbook
In the second to last sentence, I have no idea how $v = (2,0)$ was calculated. Can someone derive this for me in detail, or with a picture?
- 202
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4
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374
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Inertial and non-inertial frames in classical mechanics
Does the inertia of a mechanical system depend on the choice of coordinate systems? For example, is there a mechanical system that is non-inertial in Cartesian, but that is inertial in spherical?
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