All Questions
Tagged with motion or kinematics
4,321 questions
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Doubt about Polar coordinates
I know that for motion that does not involve rotation relative velocity of a object say $a$ with respect to $b$ can be calculated as $$\mathbb v_{ab}=\mathbb v_{ao}-\mathbb v_{bo}$$where $o$ is some ...
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votes
3
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978
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Why is the kinetic energy for non-relativistic velocities not described by $KE=mc^2$?
Today, I learned that the kinetic energy of an object can be described by
$$KE=\gamma mc^2=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}mc^2.$$
I have been taught in school that the kinetic energy of an object ...
- 13k
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1
answer
357
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Two-body decay conservation of energy
I was trying to derive transition rate for a two-body decay process. In one of the reference I'm following, it consider $a\rightarrow1+2$ decay, and said the daughter particles in center-of-mass ...
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Cross Section Formula and Delta Function Identity (Eq 4.77 in Peskin & Schroeder QFT)
In the book, while deriving the cross section formula for particles A and B, a Dirac delta appears in Eq 4.77:
\begin{align}
\int d\bar{k}^z_A \, \delta\left.
\left(
\sqrt{(\bar{k}^\perp_A)^2+(\bar{k}^...
- 21
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4
answers
147
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Are solids with the same density as air possible?
I was recently considering how to keep a super cheap ultrasonic range sensor safe from balls (or blocks, or whatever) going down ramps (or otherwise moving at high speeds) in a physics lab. It struck ...
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5
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Why is the velocity on the top of a wheel twice the velocity of its axle?
When a wheel is rolling, not skidding, and its axle moves at velocity $\vec{v}$, then a point on the top of its circumference will move at velocity $2\vec{v}$, shown below.
I really don't understand ...
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142
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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 ...
- 12.9k
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4
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85
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Why is the direction of friction inwards in a rotating disc even though there is no motion in the inward direction?
So, I was studying circular motion and I learnt that when an object is placed on a rotating disc, friction acts inwards to provide the necessary centripetal acceleration and facilitates the circular ...
- 39.5k
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 $\...
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3
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Projectile motion rearrangement
So given basic knowledge about projectiles, the equation for a projectile's initial horizontal speed $V_x$ can be expressed as $V\cos\theta$, $V$ being the initial velocity. Then the horizontal ...
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1
answer
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Adding equations of motion
Consider an object of (constant) mass $m$ subject to forces $F_i$ where $i=1,\ldots,n$. Now assume $s_i, v_i, a_i$ are the corresponding equations of motion (position $s$, velocity $v$, acceleration $...
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3
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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 $t = 45$ ...
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Calculation of displacement field from a strain field
I am trying to calculate the displacement field from a given strain field in 3D. It is quite a cumbersome calculation, as presented in Applied mechanics of solids by Bower;
\begin{equation}
u_i(x) ...
- 11
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2
answers
74
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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 ...
- 60.4k
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vote
1
answer
59
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Is the Doppler Effect for sound waves with a moving source due to the fact that the wave speed is independent of the source?
The Doppler Effect is typically formulated as follows:
$$f' = \dfrac{v \pm v_o}{v \mp v_s} \cdot f$$
The reason for the frequency increasing for observer moving towards source seems clear enough. It ...
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2
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54
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The No Slip/Slip Condition for Rotating/Rotating and Translating Bodies
Consider a sphere of radius $r$ that is rolling on a rough surface, where its translational velocity $v$ is equal to $\omega r$, where $w$ is the angular velocity of its rotation. In this case, I ...
- 99.9k
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1
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266
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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 ...
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votes
1
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306
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Circular motion at relativistic speed
I am working on a personal hard science-fiction project but when I analysed the following situation, in the context of special relativity my conclusion seems counter intuitive and perhaps I am ...
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1
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Interpretation of a motion in continuum mechanics with a spatial description
in the book introduction to continuum mechanics 4th edition (Michael Lai, second chapter), there is an exercice about a motion of a continuum (exercice 3.2.1).
the motion is $$x1 = X1 + k.t.X2 ;$$
$$...
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0
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24
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Energy in projectile motion
When approaching a projectile motion problem using the conservation of mechanical energy, why do we use the speed of the object as a whole and not only the vertical component?
The horizontal motion of ...
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0
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29
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Shifting a relative coordinate system
I've been working on recreating Boston Dynamics' Spot for the past few months. After addressing the kinematics, I've encountered a significant issue. The way I've set up the leg positions has severely ...
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1
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275
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Time to travel a set distance given variable acceleration
Trying to solve a problem for the acceleration of an automated shuttle car at my work, been a while since I studied this stuff so thought I'd reach out for help.
I have a shuttle car that is tasked ...
- 213k
2
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1
answer
247
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How to calculate jerk in uniform circular motion?
We can calculate the centripetal acceleration in circular motion by the equation v^2/r. But how do we calculate the jerk (which is acceleration over time)?
- 482
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2
answers
71
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Vector form of kinematic equation for motion with constant deceleration
Here is the equation for finding the velocity in the case of constant acceleration:
$$\vec{v} = \vec{v_0} + \vec{a}t$$
Hence by integrating this equation with respect to t, we obtain position equation:...
- 131
1
vote
1
answer
217
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Shear strain of a fluid element
I am going through the derivation of the shear strain rate formula for a fluid element and ran into a point of confusion. In the figure below, the change in angle that occurs as the line segment $BC$ ...
-2
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1
answer
49
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Speed of atoms being pushed away
It is said that it is impossible to calculate one-way speed of light.
I have doubts in my small theory and I would like someone to correct me because I lack in knowledge in physics, and I'm surely ...
- 213k
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vote
2
answers
32
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Please help find my error in comparing two acceleration equations
Please help me figure out where my mistake is when comparing two acceleration formulas and coming up with $4x^2 = x^2$. Thank you in advance.
The Kinematic Equations say:
$v^2 = v_0^2 + 2aΔx$
$Δx = ...
- 112
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3
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102
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How acceleration affects velocity?
I understood that the acceleration changes the velocity and the velocity changes the position.
So I tried to calculate the position of a falling object, where $y_{acc} = 9.81$ and the initial values ...
- 60.4k
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1
answer
88
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Why is the derivative of the distance between two points not their relative velocity?
I have a problems where I wish to calculate the relative velocity between two objects, and the answer to the problems says that a component of the velocity is second order and hence can be dropped. ...
- 8,778
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2
answers
131
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How does a sphere roll on ground, no really?
Everyone knows this right!
Consider the ground to be the $xy$ plane and consider gravity to be acting along the $-z$ direction. If a sphere (mass $M$, radius $R$) is placed on the ground and given ...
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2
answers
31
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Do these two refer to the same reference frame? [duplicate]
What exactly is the difference between a reference frame and a coordinate system (with respect to classical mechanics only)?
Can we claim that these two coordinate systems is from same reference frame?...
- 213k
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0
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35
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Spinning top moving in curved spacetime
If I have a spinning top in empty space, it would take work to change the orientation of the angular momentum vector of the top. Suppose I throw a spinning top in flat space such that the direction of ...
- 1,254
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1
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42
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Spinning mass around Spring with gravity
I've seen similar posts, but none in which a mass rotates vertically while connected to a spring, with gravity acting on the mass. I want to know if the path of the mass can be described with ...
- 500
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1
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76
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How do force and mass work with all derivatives of position?
I think if $F(t) = kt^0$ then $$x(t) = x_0 + v_0t + \frac{k}{m}\frac{t^2}{2!},$$ and if $F(t) = kt^1$ then $$x(t) = x_0 + v_0t + \frac{k}{m} \frac{t^2}{2!} + \frac{k}{m} \frac{t^3}{3!},$$ and so on, ...
- 12.9k
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1
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338
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How to calculate traveled distance with non-constant acceleration in time? [closed]
I know this formula $D = vt + \frac{1}{2}at^2$ for calculating the distance given initial velocity, time and acceleration. But what if my acceleration is not static, but increasing exponentially ...
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votes
2
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623
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Is there a relationship between the magnitude of the velocity and acceleration vector?
Given a path, how do the magnitude of the velocity and acceleration vector along the path correlate? I am confused due to the fact that the acceleration is the change of velocity over time and in ...
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2
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7k
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Distance formula in kinematics?
I've always seen it $d = v_i t + \frac{1}{2} at^2$
However, I also saw it as $d= d_i + v_i t + \frac{1}{2} at^2$ where $d_i$ = initial position. This was applied to 2D kinematics. Can anyone explain ...
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4
answers
1k
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How do I know if a motion is 1 dimensional or 2 dimensional?
If an object is moving in a straight line with an angle with x axis (it may be vertical or horizontal) , is it 1 dimensional or 2 dimensional?
The question was asked by my teacher and he himself gave ...
- 39.5k
2
votes
2
answers
411
views
What's the best answer to "how many bounces until the ball stops"?
A problem question that has been coming has the form:
How many complete trips between two plates moving towards each other can you make? (Given that you are moving between them at a constant velocity,...
- 12.9k
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0
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48
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Draw the angle graphically [closed]
Hi everyone (sorry for the "unclear" title), I'm having trouble graphically representing the point of this:
A stone is thrown from the top of a tower with $h = 50\text{m}$ and with a ...
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1
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43
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Work Done by kinetic friction in Circular Motion
We know when an object is moving in a circular motion on a rough horizontal surface, direction of kinetic friction is constantly. Thus, fto calculate the work doen by friction, we need to use ...
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1
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53
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Is the answer given in the option wrong? [closed]
The question is
"An Object moves along a straight line. The graph illustrates how the acceleration of the object changes with time. The direction of the motion of the object changed only once, ...
- 213k
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votes
1
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60
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Strain energy stored in a bungee cord pulled at its midpoint [closed]
A bungee cord that behaves elastically has an unstressed length $L=.76$ m and a stiffness $k=140$ N/m. The cord is attached to two pegs, distance $b=.38$ m apart, and pulled at its midpoint by a force ...
- 77.9k
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5
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135
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What does it mean when vector quantity is negative?
I’ve seen in some problems that vector quantity is negative. For example, negative Coulomb means that two charges attract… negative acceleration means that object is slowing down. However, magnitude ...
- 99.9k
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votes
4
answers
169
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Motion of person in bus in inertial and non-inertial frame
A person is sitting in a bus that is moving with constant velocity, due to friction their is no relative velocity between bus and the person.
Suddenly the bus starts to move with a constant ...
- 77.9k
1
vote
2
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101
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What is the correct way to think of position?
How accurate would it be to think of position (along some axis) as the component of radius vector. Example:
$$ \textbf{r} = x \hat{\textbf{i}} + y \hat{\textbf{j}} $$
And if that is correct, we could ...
- 3,347
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1
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45
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How to calculate the relative speed when three bodies are involved? [closed]
Two trains A and B start from a station and move in parallel tracks with velocities 40 kmph and 60 kmph respectively. A man sitting in train A. watches a lady who walks inside the train B at a speed ...
- 14.9k
-1
votes
3
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69
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Different results of Range of a projectile [closed]
My question is from the Range of a projectile. Range is displacement of the projectile through X-axis. We all know the formula for the range $R$ of the projectile is $$R=\frac{v_0^2\sin(2\theta)}{g}$$ ...
- 77.9k
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82
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How much time does it take for an object to fall from space? [closed]
Let's say there's an object of mass $m$ in space, $h$ meters away from the surface of the Earth. $h$ is large enough that $g$ cannot be assumed to be constant. The acceleration varies according to ...
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2
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2k
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Aim lower from high elevation?
I've heard you must aim lower relative to the target (possibly below it??) when shooting from an elevated position versus shooting from the same level as the target. How can this be?
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