Questions tagged [kinematics]

The description of the movement of bodies by their position, velocity, acceleration (and possibly higher time derivatives, such as, jerk) without concern for the underlying dynamics/forces/causes.

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Can change in position due to acceleration be expressed using dual quaternions?

Dual quaternions seem like an appealing way to model 6DOF motion since they linearize rotation. I've reviewed what literature I can find on then, and found expressions for translation and change in ...
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What are the scalar equations for velocity and displacement if acceleration obeys the inverse-square law?

In basic high school physics/calculus you learn that you can formulate equations for velocity and displacement under constant acceleration as: $a(t) = a_0$ $v(t) = a_0t + v_0$ $x(t) = \frac{1}{2}...
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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 ...
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In real life, why is space of states or state-space defined only by position and velocity?

My book defines state-space as "the collection of all possible states of the system." For example, the state-space of a coin is heads or tails. It also said that in our world, state-space is defined ...
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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? ...
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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? ...
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272 views

Is there some intuitive way to think about imaginary time?

When acceleration is constant, then distance is a quadratic function of time. So, the solutions can be complex numbers, right? I can intuitively think of negative solutions like this: If my scooter ...
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Confused about summing over the velocity squared term

Consider a cubical box, L on each side. The box contains N molecules of ideal gas, each of mass m. All collisions are elastic. The force exerted by one molecule when it collides with a wall of ...
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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 ...
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2answers
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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 $v$ ...
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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 ...
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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 ...
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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 ...
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354 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 ...
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irreversibility Aristoteles law of motion

I am watching the second lecture from the theoretical minimum and do not understand the argumentation of Susskind. For those who do not want to watch the video. It is about the law of motion from ...
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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 ...
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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 ...
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139 views

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 ...
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538 views

What does kinetic energy at infinity mean in terms of supernovae?

I have noticed that in some paper that the term "kinetic energy at infinity" is used. I understand what potential energy with reference to infinity mean, but what does the term kinetic energy of ...
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366 views

How to model an accelerometer measurements on a car wheel?

I am working on kinematically modelling an accelerometer on a car wheel. When working on the initial conditions, I am confused whether or not I should use the gravitational acceleration since there ...
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820 views

How do I find equations for the distance of the planets relative to one another?

I know I should be able to piece together some basic Newtonian equations for this, but I'm not sure where to start. I want to be able to choose one planet as the center and calculate its distance ...
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2answers
222 views

Water flow in salt solutions contemporary exposed to an electrical and constant magnetic field

When a permanent magnet is held motionless close to a salt solution which already has been exposed to an electrical field a flow in the water will be induced and can be detected by applying some ...
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1answer
119 views

Are there bounds or measurements on the derivative of acceleration (jerk)

The title says it all. Is there a physical maximum value to the 3rd derivative of position? Common Lore says that there is not and that jerk does not play any role in physics. My guess is that there ...
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Having some trouble with acceleration in polar coordinates

So, I solved a question about acceleration in polar coordinates, but most people in my class (Classical Physics, first year at university studying Physics) disagree with my answer. So the question is ...
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Energy spectrum of photoneutrons

In "Radiation Detection and Measurement" Knoll considers the production of neutrons by a ($\gamma$, n) reaction such as \begin{align} \gamma + \ ^{2}_{1}\text{H} \rightarrow \ ^{1}_{1}\text{H} + n &...
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Why is water in the asymmetric cylinder not capable of Simple Harmonic Motion?

I'm learning physics in a high school. I'm curious why water in the asymmetric cylinder is not capable of SHM. I've learned that water in a symmetric cylinder can make a Simple Harmonic Motion. But ...
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Relative kinematics curved space

I know that in a general curved manifold it is possible to describe parametric curves. Then, the length of the curve will be a indipendent from the coordinate system used --> the metric tensor ...
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1answer
118 views

Why does tension in string become zero when it is at the top most point in a vertical circle?

In the question to find out the minimum speed of a stone fastened to a string at the top most point in a vertical circle, we consider tension $T$ to be zero and equate $mv^2/r$ to $mg$. But isn't it ...
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How to find force needed to lift two wheels off ground during cornering?

I'm attempting to calculate the maximum velocity at which I can safely drive around a corner. One scenario I'm considering is where all four wheels maintain contact with the ground, but slips. The ...
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1answer
49 views

Theoretical question regarding two elliptic trajectories

I am new to Newtonian Mechanics, and I was wondering regarding the following: Are $$\vec{r}(t): a \sin(ωt)\hat x +b\cos(ωt)\hat y$$ and $$\vec{r}(t): a \sin(ωt^2)\hat x +b\cos(ωt^2)\hat y$$ ...
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Car Max Range Equation

In space engineering, thanks to the rocket equation, if you know some properties about a rocket (payload, fuel mass and specific impulse) you can compute the theoretical maximum distance the rocket ...
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79 views

Dimensionally inconsistent!

This equation doesn't seem to be correct. Dimensionally inconsistent, in fact! How then, is it established? $$s_{t}=v_{0}+\frac{1}{2}a(2t-1)$$ (In case you don't know, this is the equation used to ...
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1answer
36 views

Calculate the kinetic friction velocity vector from the kinetic friction force in a simulation

I am doing (programming) a simple kinematic 2D simulation on blocks. The idea is that the block will have a force applied. 1) From the force and mass I calculate the the acceleration vector (will ...
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1answer
58 views

Ideal geometry for a shaft terminating thrust bearing

Following this PyDy example, I'm trying to understand the problem set 3.10 of the book: Kane, Thomas R., and David A. Levinson. Dynamics, theory and applications. McGraw Hill, 1985. page 272 (292 ...
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89 views

Doubt in kinematics (equations of motion)

Suppose a paticle travels from $A$ to $D$ inscribing a path like the one shown in the picture taking time $t$. My question is if I apply the equation of motion, which is $$s=ut + \frac 1 2at^2$$ ...
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1answer
50 views

Calculating acceleration of an object using $x$, $y$ and $z$ coordinates

I have x, y and z coordinates for a test I had carried out for a tool. I had an accelerometer installed on the tool and I used two types of motion to move the tool, rotation and translation. Right now ...
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Does the proper four-acceleration $A^{\mu} = (0,0)?$

Let the proper four-position vector $x^{\mu}(\tau) = (0, \tau)$. Differentiating this successively wrt $\tau$ I get the four-velocity $u^{\mu}(\tau) = (0, 1)$ and then the four-acceleration $A^{\mu}(\...
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The Electro-Dynamics of Moving Bodies

In his original paper ''On the Electro-Dynamics of Moving Bodies'', in presenting the case of a rod AB moving with velocity v in a stationary system or frame K, Einstein states that the time interval ...
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Can I solve this electric forces question by integrating velocity with respect to displacement?

In my physics tutorial for electricity, there was one question in particular that struck me as interesting. It is as follows: One particle has a mass of $3.00\times10^{-3}$ kg and a charge of $+8....
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Ball dropped from building question

So in one of my physics books, under the free fall section, it was written A ball is dropped from a building of height $h$, speed $u=0$ and it reached ground after time $t$. From the same ...
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81 views

Meson scattering amplitude in the linear sigma model

I am trying to calculate scattering amplitudes with linear sigma model Lagrangian, given as $$\mathcal L= \frac{1}{2}(\partial_{\mu}\sigma)^2+\frac{1}{2}(\partial_{\mu}\vec{\pi})^2-\mathcal U(\sigma,\...
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3-particle phase space in $d$ dimensions

recently I came across a problem concerning the 3-particle phase space. I am trying to show, that the 3-particle phase space for massless particles with momenta $p_1$, $p_2$ and $k$ is given by $$ d\...
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1answer
133 views

How to calculate time at which two circles will touch?

Hopefully this is the right... Stack to ask this at. Apparently there are a bunch of them. I'm trying to find a formula to detect the time at which two circles in a 2d plane will touch. I'm given the ...
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39 views

Electromagnetic propulsion

Is it possible to convert energy in magnetic field of a solenoid into acceleration of a magnet going through that solenoid ? My experiment was to look at the effect of current intensity on the ...
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79 views

exchanged momentum in Compton scattering

I am trying to resolve a confusion regarding scattering kinematics. I am considering Compton scattering, i.e. a photon with four-momentum $k$ scatters on an electron with four-momentum $p$, the final ...
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2answers
142 views

Are distance and displacement always frame independent?

I'm aware that distance and displacement, both are independent of reference frames, when the two frames are stationary wrt each other. Because the actual distance (or the shortest distance) between ...
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193 views

Energy consumption from acceleration

I have an interesting problem. I have a machine which has to lift 35 kg (this is the total mass of the object and the lifting arm). The lifting is done by a servo motor. Now I want to calculate the ...
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How should I think about a block-and-tackle configuration weight-lifting machine?

At my gym, some of the weight machines provide a double mechanical advantage using a gun tackle pulley configuration. For a long time when I was using such machines, I convinced myself that if I were ...
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Move body in 1-dimension to desired state by applying force

Consider a simple point mass of $M$ in vacuum in 1-dimension with initial position $x_0$, velocity $v_0$ and acceleration $a_0$. Our goal is to move this body to position $x_1$ with velocity $v_1$ and ...
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1answer
29 views

Is there a transport equation specially for two rotating frames?

The classical transport equations related vector derivatives between an inertial frame and a rotating frame, is this equation applicable to a set of frames where both are rotating? or does one always ...