All Questions
Tagged with motion or kinematics
489 questions with no upvoted or accepted answers
6
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0
answers
376
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Upper bounds on phase space momenta
Suppose I wish to calculate the phase space volume for the process $\overline{X}X \to A_1 A_2 A_3 A_4 A_5$ in the CM frame of $\overline{X}, X$ so that $\sqrt{s} = 2m_X$. The volume is given by
$$
V \...
- 4,820
4
votes
0
answers
166
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Why is the ratio of components of kinetic energy equal to the ratio of kinetic energy to total energy for a projectile whose range is maximized?
The launch angle $\theta$ that maximizes the range of a projectile in a uniform gravitational field is
\begin{align}
\theta = \arctan\left(\frac{v_o}{\sqrt{v_o^2 + 2gh}}\right), \tag{1}
\end{align}
...
- 41
4
votes
1
answer
68
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Transformations and kinetic energy
From the equation $E_k=\frac12mv^2$ you can determine more energy is necessary to accelerate a mass the higher your initial velocity is. For example, three times more energy is necessary to accelerate ...
- 127
4
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3
answers
4k
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Projectile, air resistance and wind
So for my school project I am working on a projectile simulator and air resistance.
So I have looked at this.
Equations for an object moving linearly but with air resistance taken into account?
...
3
votes
0
answers
118
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Is there a software that computes simple particle decay kinematics?
I was trying to figure out some details about a specific decay channel for a generic particle accelerator experiment. For instance if I have a proton proton collider with fixed energy, I would like to ...
3
votes
2
answers
160
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Acceleration in terms of displacement
I am having problems understanding the derivation of acceleration in terms of displacement. The first step is fine:
$$a(x) = \frac{\mathrm dv(x)}{\mathrm dt}
= \frac{\mathrm dv(x)}{\mathrm dx} \frac{\...
- 131
3
votes
1
answer
242
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Kinematics of a rolling disk on a static disk (variation of the Euler disk)
I'm puzzled by the following problem. Consider a simple tilted disk $\mathcal{D}$ of radius 1 (in any unit) rolling without sliding on top of a static horizontal disk $\mathcal{S}$. The normal $\...
- 7,677
3
votes
1
answer
236
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Dark matter thermally averaged cross section
I'm trying to rederive the results of this classic paper:
https://doi.org/10.1016/0550-3213(91)90438-4
to find the thermally averaged cross-section. I am struggling with a change of variables and ...
- 357
3
votes
0
answers
100
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Momentum Vectors in Bondi coordinates
In the Bondi-Sachs formalism, we can define the notion of 'retarded' time via a coordinate transformation of the usual Minkowski metric
$$
d s^{2}=\eta_{\mu \nu} d x^{\mu} d x^{\nu}=-\left(d x^{0}\...
- 2,494
3
votes
1
answer
142
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A situation to compare time taken by two objects
This randomly came up in my mind.
suppose a bead like particle P at A in a frictionless hemispherical bowl. It is released from A at t = 0. A horizontal velocity v is imparted to bead P. A bead Q of ...
- 1,200
3
votes
0
answers
398
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Possible to convert accelerometer $x,y,z$ measurements into quaternion?
I have an inertial measurement unit (IMU) with an accelerometer that reports the acceleration (a) along the $x$, $y$ and $z$-axis in milli-$g$. I can get the Euler angles for roll ($\phi$) and pitch ($...
- 31
3
votes
0
answers
62
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Why does the photon in Compton Scattering have a minimum frequency/maximum wavelenght?
Using conservation of four-momentum one finds that, with respect to the angle of deviation of the photon from its original direction $\theta$, the wavelength and frequency of the emitted photon are:
$
...
- 423
3
votes
0
answers
419
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Is there is an entropy cost of moving an object?
Is there an entropy cost associated with moving an object from one point to another, even if all forces involved are conservative? Or, is there some condition on what kind of move has an entropy cost?
...
- 33.4k
3
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0
answers
261
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Heads, Tails... Edge?
No Nobel prizes at stake, but just an idle thought and an idle question.
How could one calculate the probability of a flipped coin landing stable on its edge, instead of heads or tails? I assume ...
user56903
3
votes
2
answers
1k
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Rod's Kinetic Energy in the pendulum problem
On the MIT OCW for engineer dynamics the cart pendulum problem is solved by using the Lagrange Method here. This is a 2D problem, so rotation only occurs on the Z axis. While obtaining the rotational ...
- 31
3
votes
3
answers
1k
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Upstream and downstream problem using relative velocity
On a river coast, there is a port; when a barge passed the port, a motor boat departed from the port to a village at the distance $S_1 = 15$ km downstream. It reached its destination after $t = 45$ ...
2
votes
0
answers
72
views
Best way to calculate velocity, acceleration and jerk with different temporal resolutions
I have body motion tracking data I am using for my thesis. I am trying to find relationships between the kinematics of the body of speakers, and the acoustic measures of their speech (e.g. speech ...
- 21
2
votes
0
answers
142
views
Decay of a particle with nonzero momentum into 2 particles: Why are there two solutions?
I am trying to solve a decay of a massive particle into 2 massless particles in the lab frame. I am not interested in the typical solution of boosting the system in the rest frame of the parent ...
2
votes
2
answers
74
views
Does angular absement exist?
Probably a dumb question. I'm a highschool student, and I don't even know if it is even possible to integrate an angle (for reference, I haven't even learnt integration yet at school, my calculus ...
- 31
2
votes
1
answer
65
views
Intercepting a moving target with limited change in velocity
I have an already moving object A trying to intercept a moving target B in 3D space, and I have limited acceleration (for example not necessarily enough fuel for the optimal acceleration).
A is ...
- 23
2
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0
answers
80
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Equation of Motion of Rigid Body Represented by Twist and Derivative of Twist
This question is an extension of question Understanding terms Twist and Wrench.
Assuming there is a rigid body with body twist denoted as $\mathcal{V}_{b}=\left(\boldsymbol \omega_{b}, \boldsymbol v_{...
- 21
2
votes
1
answer
83
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With constant acceleration, can $\bar{v}=\Delta{x}/\Delta{t}=(v_i+v_f)/2$ be established rigorously without calculus?
I have found no way to rigorously establish the basic one-dimensional kinematic equation relating the two following expressions of average velocity without using some kind of argument that amounts to ...
- 2,052
2
votes
1
answer
78
views
Relationship between tangential and angular acceleration in 3D
In 3D circular motion, $\vec v=\vec \omega \times \vec r$, then the tangential acceleration is
\begin{eqnarray*}
\vec a_t =\frac{d \vec v}{dt} & = & \frac{d}{dt}(\vec \omega \times \vec r)\\
...
- 31
2
votes
0
answers
53
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Is this derivation of the relation between the momentum and energy of a photon correct?
$$E=\int Pdt$$ where P is power
$$E=\int F⋅vdt$$
$$E=\int\frac{dp}{dt}\cdot vdt$$
$$E=\int vdp$$
Since the velocity and momentum are in the same direction, the dot product is equal to the product of ...
2
votes
0
answers
83
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Confusion about changing frames of reference in loop integral
I have what seems to be a pretty stupid problem I've been stuck on for days.
Consider a three-point, one-loop interaction like the image below. For example, it could be a higher-order contribution to ...
- 41
2
votes
0
answers
183
views
Proving that the relative angular velocity of any particle with respect to any other particle is the same in a rigid body
Claim: The angular velocity of any point mass of a rigid body relative to any other point mass is the same, i.e., $\vec{\omega_{i,j}} = \vec{\omega}\;\,\forall{i}\,\forall{j}$, where $\vec{\omega}$ is ...
- 41
2
votes
1
answer
266
views
Given a path and maximum acceleration, what is the minimum time to reach the end?
As stated in the title, I want to find an expression or a way to calculate the minimum time to go from one point of a path to another when the path is given and acceleration is restricted.
Thus far, I ...
- 121
2
votes
1
answer
44
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Weight of Diamagnetic Objects in Lenz Effect
I've seen the simple experiment of dropping a neodymium sphere down through a copper or aluminum tube where it falls at less than g. The "Lenz Effect"
My question is:
Has there ever been an ...
- 111
2
votes
0
answers
50
views
How do kitesurfers / kiteboarders move?
Explanations I've managed to find on the web either focus on how to practice the sport or how a kite flies. A full force vector decomposition that makes clear how downwind, upwind, and crosswind ...
- 359
2
votes
0
answers
33
views
Are quantum dot’s immobile?
In a recently closed question regarding the cooling of quantum dots through lasers has one of the commentators state that this is in fact impossible as QD’s are immobile:
Can quantum dots temperature ...
- 487
2
votes
2
answers
156
views
Derivation of $E = mc^2$. Difference between $KE$ and $E$?
I was following a derivation of $E = mc^2$ in this video: https://www.youtube.com/watch?v=KZ8G4VKoSpQ The relevant parts are from 18:00 - 23:18.
I was perplexed at how the narrator introduced $E$. He ...
- 163
2
votes
1
answer
909
views
Particle momentum in collision expressing in Mandelstam variable
Consider the $s$-channel process. I use the metric convection $(+,-,-,-)$. The constraints are: Conservation of four momentum: $p_{1}^{\mu}+p_{2}^{\mu}=p^{\mu}$ and on mass shell condition $p_{i}^{2}=...
- 591
2
votes
1
answer
107
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Usefulness of the Instantaneous Axis of Rotation in Robotics
Hello Physics Exchange,
I finally have some decent understanding of the concept of instantaneous axis of rotation in the context of a single rigid body but I am still trying to piece together why it ...
- 93
2
votes
1
answer
41
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Given a fixed quantity of work performed, what choice of momentum will maximize how deeply a nail is driven into wood?
Let's say I am trying to drive a nail into a piece of wood by dropping a weight on it.
I am willing to do some fixed quantity of work to raise up the weight. I can choose the weight and the height, ...
2
votes
1
answer
606
views
How to determine the minimum "Arrival Distance" given a maximum velocity, acceleration and jerk along with an initial velocity and acceleration?
Problem
Given the following:
$A$ - maximum acceleration.
$J$ - constant jerk (the rate of change of acceleration).
$v$ - initial velocity.
$a$ - initial acceleration (where, in practice, $a ∈ [-A, A]$...
- 121
2
votes
1
answer
113
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Do things get brighter as they travel faster and if so what would the general equation to model that be?
I'd like to preface this by saying that I am not talking about glowing caused by the heat generated from air resistance. Instead lets just say that the hypothetical object we're talking about it in a ...
- 135
2
votes
0
answers
153
views
Why the material time derivative of a material field $F$ equals to the directional derivative of $F$ in the direction of the velocity vector $v$?
I am reading the book Nonlinear Solid Mechanics A Continuum Approach for Engineering by Gerhard A. Holzapfel, Chapter 2.3 and find one equation confusing, which is displayed in the pitcure.
Here in ...
- 53
2
votes
0
answers
427
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$s$-channel, $t$-channel and $u$-channel
I'm studying the $e^{+}e^{-}\rightarrow f^{+} f^{-}$ scattering, where $f$ is a generic fermion ($f^{\pm}\not=e^{\pm}$). I know the process is described by the $s$-channel, but why the $t$-channel or ...
- 21
2
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0
answers
1k
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What am I not understanding about this double integration of acceleration to get position?
Brilliant.org has a module on classical mechanics and I'm having difficulty with a mathematical step. They want you to represent position in terms of acceleration and then to solve the double integral ...
user158309
2
votes
0
answers
81
views
Physics of a catenary with sinusoidal motion at one end
If we have a catenary line with a mass per unit length of m with one end fixed and the other end moving in sinusoidal motion like $A.sin(\omega.t)$, how would I ...
- 121
2
votes
2
answers
152
views
Definition of velocity in classical mechanics
Let $(r_1,r_2,r_3)$ be the coordinates of a particle $r$ in the coordinate system $\phi$. Let $\{\hat{e_1},\hat{e_2},\hat{e_3}\}$ be the coordinate basis of $\phi$. Why do we define the velocity $v$ ...
- 350
2
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0
answers
66
views
Motion of a catapulted point mass moving freely inside a spherical bucket
I am trying to study the motion of a point mass inside the bucket of a catapult.
The catapult is shooting downward (i.e. describing a rotation of 180° from the horizontal axis) and I would like to ...
- 51
2
votes
4
answers
1k
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Uniform Circular Motion w/ Tension and Friction
So I had a problem today which I couldn't make any sense of. I don't have access to it at the moment but this is a pretty accurate approximation.
Basically, a mass (m) is swinging horizontally on ...
- 21
2
votes
0
answers
170
views
Branching ratio for a bound state
Consider the meson $\Upsilon(10860)$. It decays into $B\bar{B}$, $B\bar{B}^*+cc$ and $B^*\bar{B}^*$. The mass of $B$ is $5.28 ~\textrm{ GeV}$ and mass of $B^*$ is $5.33~\textrm{ GeV}$. The branching ...
- 1,558
2
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0
answers
98
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When this CD is spun so fast that it shatters, why does the warped shape move slower than the surface?
In this video where a CD is spun abnormally fast to the point of shattering, one notices from the writing on the CD that the surface is spinning faster than the warp "shape" is. In other words, the ...
- 21
2
votes
1
answer
125
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Vector Derivative: General Case
From "An Introduction to Mechanics" by Kleppner & Kolenkow, SIE-2007, Chapter 1 (Vectors and Kinematics), Section 1.8 - "More about the derivative of a vector".
In this section, towards the end, ...
- 203
2
votes
0
answers
384
views
How do I model the motion of a particle changing acceleration vector (2D)?
I want to model a particle with an arbitrary initial velocity, and estimate the time it takes to reach a final point given a constant magnitude of acceleration. It should take the quickest path to the ...
2
votes
0
answers
526
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Dynamics and kinematics of quantum field theory
What is the difference between dynamics and kinematics of quantum field theory? I read that in QFT there is no possibility to keep the two things distinct because of a problem with the separability of ...
- 582
2
votes
0
answers
50
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Motion decomposition (Relativistic case)
When an electron moves at very close at $c$ (speed of light), is it physical to decompose the motion in two other directions (like what we do in classical case). If so, the motion in each direction ...
- 41
2
votes
0
answers
145
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How Burmester's theory converts rotary motion of the crank to linear movement?
I have been studying the mechanism of Klann's Mechanical spider and there it was written that by Burmester's theory it converts rotary motion of the crank to linear movement. I tried searching but how ...
- 1,850