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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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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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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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,...
- 1,771
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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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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 ...
- 1,771
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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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337
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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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0
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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
-3
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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 ...
- 7
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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