All Questions
Tagged with classical-mechanics reference-frames
204
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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 $l$ ...
4
votes
1
answer
61
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Moving body is collided with a spring system.Why there is a difference in maximum compressed distance for different observers?
Suppose a body of mass m moving with velocity collides with a spring system.The event is being observed by two observers, one at rest and one moving with a velocity v opposite direction to that of the ...
- 538
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64
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Find the equation for the angle $\theta$ in which the particle leaves the semicircle. No Friction [closed]
I think I missed something in this mechanics problem.
We're given a polished (no friction) and homogeneous hemicircle which has mass $M$ and a particle of mass $m$ laying on the top of it.
There is ...
- 153
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89
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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(\...
- 15
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2
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264
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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 ...
- 23
1
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1
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148
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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 ...
2
votes
1
answer
170
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Why is this hamiltonian not the energy? [duplicate]
Let a pendulum of length $\ell$ be connected to a rod that rotates with constant angular velocity $\omega$. $\theta$ is the angle of the pendulum wrt $z$ axis ($z$ axis is parallel to the rod).
I ...
- 980
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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 & ...
- 57
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2
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101
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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
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334
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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\...
- 27
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126
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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 ...
- 67
2
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2
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77
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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 ...
- 493
0
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419
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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 ...
- 29
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520
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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 ...
- 343
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437
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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 ...
- 1,260