All Questions
Tagged with classical-mechanics reference-frames
204
questions
0
votes
1
answer
89
views
Time derivative relation between two rotating frames
I know that the time derivative of some quantity $r(t)$ in a rotating frame which rotates with angular velocity $\Omega(t)$ is related to the derivative in a fixed (i.e. inertial) frame by
$$
\Big(\...
- 9,381
1
vote
2
answers
264
views
Finding latitude of landing of projectile in Rotating Earth
Assuming that the Earth is a uniform sphere of radius $R$, rotating about its axis with a uniform angular velocity $\omega$. A rocket is launched from the Equator in a direction due North. If it keeps ...
- 1,665
1
vote
1
answer
149
views
Lagrangian formalism for non-inertial reference frames
I was solving the exercise where the massless ring with radius $R$ is rotating around axis (shown in the picture) with angular velocity $\omega$. On the ring is a point-object with mass $m$ which ...
- 12.4k
3
votes
2
answers
121
views
Why are you allowed to omit the $V^2$ term in the non-inertial frame?
I'm trying to find trying to find the Lagrangian and Hamiltonian for a particle in a non-inertial frame, but when I try to do so, I always get a quadratic term, which textbooks like Landau & ...
- 21.9k
1
vote
2
answers
288
views
In general, conservation laws do not hold whenever the center of mass of the system is moving?
I am currently studying Classical Mechanics, fifth edition, by Kibble and Berkshire. Problem 3 of chapter 1 is as follows:
Consider a system of three particles, each of mass $m$, whose motion is ...
CommunityBot
- 1
1
vote
2
answers
101
views
How would a game of (American) football work on a space station generating artificial gravity by using spin? [closed]
Using rotation to generate artificial gravity is pretty common in sci-fi. I know the TV show "The Expanse" features it on the Mormon's vessel. I also remember a small-scale rotating space ...
- 1,666
1
vote
2
answers
337
views
Frames of references and coordinate systems
In linear algebra, a vector can be represented by different bases. However, this is merely a different representation of the same entity; i.e. $\vec x = x\hat\imath + y\hat\jmath + z\hat k = x'\hat\...
- 13.1k
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 ...
2
votes
2
answers
77
views
Total force needed to maintain constant acceleration of a bus
Suppose there is a person wearing roller-skates, inside a bus ( to neglect the friction on the floor ). The mass of this person is $m$ and the mass of the bus $M$.
Suppose, the bus now starts to ...
0
votes
1
answer
420
views
Kinetic Energy of pendulum with moving support
I am trying to calculate the kinetic energy of a pendulum with moving support. I have come across two ways that could be used to calculate the kinetic energy, and although I know that the first of ...
- 103
2
votes
3
answers
2k
views
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 ...
- 2,196
5
votes
3
answers
446
views
Passive transformation, pseudo vectors and cross product
Let's consider the passive transformation i.e. inversion only of the basis vectors (coordinate axes) and all other vectors remaining the same and check if the cross product is a pseudo vector.
After ...
- 70.2k
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 ...
- 57.2k
3
votes
2
answers
770
views
Confusions about frames of reference when deriving Euler's equation of rotational motion
I am getting confused about when torques should be frame independent. My understanding is that torque is the same in all frames that are rotating at constant angular velocity. However, this seems to ...
- 38.7k
3
votes
1
answer
1k
views
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)...
- 302