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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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Does ABS increase the breaking distance of a car? [on hold]

Question: Can an ABS (Anti-lock Braking System) instead of decreasing the breaking distance actually increase it? If yes, is this its general behaviour, or only in specific circumstances? Wikipedia ...
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River crossing with pointing method [on hold]

A river is $b$ meter wide and the water is flowing with $u$ velocity. A man with $v$ velocity respective to the river water want to get to the straight other edge point (means that point is just front ...
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What forces should I apply in order to make a craft reach a point? [duplicate]

I'd like to find out a strategy for solving the following simplified problem. A small spherical craft at $t=0$ has a position and velocity vectors $\mathbf{x_0}, \mathbf{v_0}$ in a zero gravity ...
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Basic doubts about dynamics of a rod [on hold]

I have few doubts in the given solution. It says there is no force along the plane but $mgcos\alpha$ is acting along the plane ? As given, $A$ is used as orgin. Then how come x-co-ordinate of $G$ is ...
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1answer
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Need help with physics question [on hold]

A baseball player slides across the ground towards third basd. There is considerable friction, he slows down quickly. He slides a distance of 4m and then stops. Before the slide, he was moving at 9m/s....
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1answer
88 views

Surjectivity of momentum mapping

I have to show that the following mapping of momenta is surjective. The mapping $\{p_i^{\mu},p_j^{\mu},p_k^{\mu}\}\rightarrow\{\tilde{p}_{ij}^{\mu},\tilde{p}_k^{\mu}\}$ is given by $$ \tilde{p}_k^{\...
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A multiple choice question on magnetic fields and magnetic force [on hold]

On the two vertices B,C of an equilateral triangle ABC of side d on a very rough horizontal surface, two ants of negligible dimensions start in such a way that ant from C always moves with constant ...
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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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Atom Smasher Power Input Question? Please Help [closed]

If I was to put an object with 0.001 grams of mass into an LHC or atom smasher how much energy would I need to get this object up to the same speeds as a particle -(3 or 4 seconds of the speed of ...
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13answers
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Why doesn't a braking car move backwards?

The net force on an object is equal to the mass times the acceleration, $F = ma$ When I brake on a (moving) car, the net force is negative, therefore causing the resulting acceleration to also be ...
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2answers
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Does Euler number $e$ have a role in kinematics?

Euler number $e$ is often explained with the example of compound continuous interest. I was wondering if it could also be illustrated with an example about the displacement of a body (although not an ...
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3answers
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How to understand physics and formulas? [closed]

this question may sound weird but I have notised some similarities between many physics formulas like $Ek = \frac {1}{2} mv^2$ and $s = \frac {1}{2} at^2$. Is it just a coincidence or are the actually ...
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1answer
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Line element to polar coordinates [on hold]

I'm calculating the effective metric for a vortex in polar coordinates. The velocity and the potential is: \begin{equation} \mathbf{v}=\frac{A}{r} \hat{r} + \frac{B}{r}\hat{\theta} \end{equation} So:...
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Rod ring paradox in special relativity

We have a ring and a rod whose centres lie in the x,z plane. The plane of the ring is perpendicular to the z axis, and the rod is parallel to the x axis. The rod is slightly larger than the ring at ...
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3answers
75 views

If mass is doubled, how much more power is needed to sustain the same speed?

My problem involves an object completely immersed in a fluid, moving at some speed, using a certain amount of power to sustain that speed. It could be an airplane or a torpedo, among other things. (...
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2answers
41 views

Question about derivation of four-velocity vector

In order to describe a notion of rate of change of positon, in four-dimensional spacetime, we have to introduce the concept of four-velocity. So, consider the following: For a massive particle ...
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2answers
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Equivalence between $t$ and $u$ channels

Reading about QFT diagrams, I've seen examples like Bhabha scattering where the channel $u$ wasn't necessary due to the final states are distinguisable for being made of the different particles and ...
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1answer
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Kinematic Modelling with clockwise angles defined as positive

It seems when modeling a system for which an clockwise angles is defined as positive, the resulting equations become wrong. For example : In the picture below $\theta_x$, the orientation of the ball,...
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3answers
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What would be the minimum velocity of a particle performing S.H.M.?

We were asked a simple question on a test: What is the maximum and minimum velocity of a particle performing an SHM? Note here that we're talking about a generic standard SHM here. If the maximum ...
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0answers
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How to find centre of axis in spinning device using magnetometer data and accelerometer data

I've been trying to interpret data from a MEMS sensor inside a sphere that is spinning so we can find the axis of spin and rotation direction. As the device is moving and the devices initial ...
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1answer
33 views

If time was non-existent would we be able to move? [closed]

If time would stop, would we be able to move, or would we be "frozen"? also if we could move, would we be able to move at a infinite speed ?
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1answer
58 views

How does one prove the channel independent inequality satisfied by the product of the three Mandelstam variables?

How does one prove the following equation (67.5) from the BLP Quantum Electrodynamics book? The q's are the 4 momenta, and h is the sum of all four masses. Two q's written after one another in the ...
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Clarification of Components of vectors

For finding radius of curvature for a path (eg. Projectile) why do we take component of acceleration ($g$) perpendicular to velocity and not the opposite? $$\text{radius of curvature} = \frac{\text{...
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2answers
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Rocket Equation

What formula can be used in order to find the final velocity of a rocket if the time travelled by the rocket, exhaust velocity, initial and final masses of the rocket and the initial acceleration of ...
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1answer
24 views

Are my observations about the differences between average velocity and speed, in 1 dimension, correct?

I've been struggling to understand the differences between average velocity and average speed in 1 dimension; by doing some exercises I think I have figured it out, but i want to check if I'm correct. ...
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Is there ever such thing as pure rotation or translation? [duplicate]

My thoughts... Let us consider that in a given reference frame, we perceive a body moving rectilinearly (i.e. in a straight line). I suppose we can define this "pure translation", since all the ...
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1answer
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Does the projectile motion equation work if the initial height and final heights are different?

Hi just a quick question here. Does this equation work if the initial height and final height for the projectile is different? Suppose you throw a ball off a cliff and you want to find the vertical ...
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1answer
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Projectile Motion | Modify results so the projectile peak would be constant with other trials [closed]

Context Imagine, for my experiment I throw a basketball up and forward, creating a parabolic shape. Let's say that I know I applied 2 N (force), the peak of the parabolic shape from the ground is 1 m ...
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2answers
40 views

Rolling objects released from rest: time down the ramp [closed]

Since we are given the values of I for each object, I was able to calculate the KE's of each: the solid spheres had KE of $1/5mv^2$; the hollow sphere had a KE of $1/5 mv^2$, and the hoop had $1/2mv^2$...
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1answer
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When a particle keeps “accelerating” near the speed of light, is the energy gained expressed in linearly gained impulse, or relativistic mass? [duplicate]

When a particle keeps "accelerating" near the speed of light, is the energy gained expressed in linearly gained impulse, or relativistic mass?
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3answers
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How can the friction force equals to the net force in this momentum question?

Question- from https://www.physicsclassroom.com/calcpad/momentum/prob29.cfm A physics student hurls a $315-g$ ball directly into a $3.54-kg$ box which is at rest on a table top. The baseball strikes ...
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1answer
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Kinematic Equations contradicting each other [closed]

For example, there is an object that is being thrown into the air, and we need to find the time it takes for it to reach its maximum height. Here are the variables: a = -9.8 m/$s^2$ $v_i$ = 300 m/s $...
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1answer
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Newton's 2nd law of motion and mass-energy equation [closed]

According to the mass-energy equation $E=mc^2$, so $m=\frac{E}{c^2}$, but according to Newton 2nd law of motion $F=ma$, so $m=\frac{F}{a}$. Therefore $\frac{E}{c^2}=\frac{F}{a}$, or $E=\frac{Fc^2}{a}$....
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How to animate a ball rolling down an incline?

I'm using Lagrangian mechanics to come up with the equations of motion for a ball rolling down an incline. I've come up with the following two equations. $$\begin{alignat}{1} \dot{x} &= \frac{2}{...
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2answers
66 views

Confused with derivative and partial derivative

suppose $x=f(t)$ with a constant acceleration. Then does $\frac{\text d x}{\text d t} = \frac{\partial (x)}{\partial(t)}$ since the position in $x$ only changes with time? Then the acceleration in ...
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2answers
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What is function of force $F$ and work $W$?

I know that : Position $$r:\mathbb{R} \to\mathbb{R^3} \ \ \ \ \ ; \overrightarrow{r}(t)$$ Velocity $$v :\mathbb{R} \to\mathbb{R^3} \ \ \ \ \ ; \overrightarrow{v}(t)$$ Acceleration $$a:\mathbb{R} \...
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1answer
37 views

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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Transformation of opening angle in different frame of rerefence in special relativity

I have to find the minimum opening angle for the decay $\pi^0 \rightarrow \gamma \gamma$ given the energy and rest mass of the $\pi^0$. My question is that: since the center-of-mass frame's opening ...
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1answer
39 views

Interpreting derivatives

So we have a function such that the distance moved by a particle (say $s$) is proportional to $sin(Ct)$ where $C$ is a constant. Now i needed to show that the rate of change of velocity is directly ...
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1answer
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What is the general mathematical definition of periodic motion?

What is the general mathematical definition of periodic motion? My answer : Can you say that each function is in the form $ \overrightarrow{r} (t)= \overrightarrow{r} (t+T)$. it is right?
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In any potential force field, there exists at least one periodic motion of the body?

Talking about a rigid body fastened to a stationary point and located in an arbitrary potential field V.I. Arnol'd concludes that In any potential force field, there exists at least one ...
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1answer
99 views

Using $v_f = v_0 +at$ for objects in free fall [closed]

I have a question about the difference of using $v_f = v_0 +at$ and $s = v_0t + \frac{1}{2}at^2$ for objects in free fall. I'm trying to solve a problem where there's a ball rolling along an inclined ...
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0answers
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Movement expressed in polar coordinates

The movement of a certain particle in the $OXY$ plane is given in polar coordinates by means of the equations: $$p(t)=p_{0}e^{\Omega t}$$ $$\theta(t)=\Omega t$$ And I want to calculate the speed ...
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1answer
34 views

How to get the four-velocity components from a given metric tensor?

I’m a little bit confused about how to get the four-velocity components from a given metric tensor (or line element). For instance, which are the components of the four-velocity in the Schwarzschild ...
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1answer
67 views

Calculate launch angle of object moving away from view

I'm writing image processing software and my goal here is to take an image of a projectile moving away from the camera and determine the launch angle. What I already know is: The actual size of the ...
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2answers
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Relativistic space rocks. Are they possible?

I was thinking that the Universe is full of extreme events. Colliding galaxies, exploding stars, colliding planets (like in one of models of our Moon formation), colliding black holes... Can it be ...
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0answers
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How to accurate scale start velocity in projectile motions? [closed]

I have projectile motion where the angle $\alpha$ is $45^\circ$, and the start velocity is $45\ \rm{m/s}$. We can then expect it to land about $206.422\ \rm m$ away; however, if I were to change/...
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0answers
27 views

Kinematics and energy formula for hammering a ball

Let's assume you have a hammer which is unfortunately drop on a tennis ball. the tennis ball has the elasticity property. What would be the possible outcome from this? I could think one possible ...
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1answer
34 views

Which approach can I use to find the total distance travelled by the car?

I am really struggling with the following problem: A car starts from rest with constant acceleration and moves in a straight line. At some point the car passes two marked road sections of ...
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3answers
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Extracting the 3D coordinates of a moving object from a video

Take a look at these two pictures, which are stills from a video which demonstrates magnus effect in football: I want to extract the coordinates of this ball in 3D space from this video. These are ...