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3
votes
4answers
121 views

Intuitive explanation of the half in the $\frac{1}{2}at^2$ distance equation?

The full equation $$ Xf = X_o + V_o t + \frac{at^2}{2} $$ is integrated from the velocity function (which was integrated from constant acceleration function), right? The problem is, I can't seem to ...
3
votes
1answer
53 views

How to set up line integral of electric field? Confused over notation

In multivariable calculus the line integrals was parameterized and denoted: $$ \int_C \mathbf{F} \bullet \, d\mathbf{r}=\int_D\mathbf{F}(\mathbf{r}(t)) \bullet \frac{d \mathbf{r}(t)}{dt} \, dt $$ ...
5
votes
2answers
162 views

Calculating Intensity/Strength of Vibration with 3DOF

I want to calculate the intensity/strength of vibration at a given location. I have measured the acceleration at this location, using an accelerometer. So my measures look for example like: ...
-4
votes
0answers
34 views

Modulus in Calculus? [migrated]

Does Modulus function has any effect during differentiation and integration of a quantity? For example: Let two velocities be: $$ v_1= (t-2) m/s $$ and $$ v_2=|t-2|m/s $$ If we differentiate them ...
0
votes
3answers
108 views

Can we have a physics by using other mathematics except calculus? [closed]

We (I) always have been said that we don't need to real values, we just need to differences. For example, $\mathrm du=C_v\mathrm dT$ and $\Delta u=\int_{T_1}^{T_2}C_v\mathrm dT$. So, I have some ...
1
vote
0answers
11 views

Proof from Calculus 1 [migrated]

Last days, from going into a website of the university of Pisa, I found an exercise given in the previous exams, in 1999. The problem was like: Given a continuous function f in R, and which ...
0
votes
1answer
28 views

How to calculate orbit of a sphere around a bigger one in microgravity?

I don't have any knowledge in physics, but in a world building related question, I need to know how can I calculate the orbit or the distance in each point of the orbit around a spherical object in ...
3
votes
3answers
91 views

Why we use differential element to get general form? [closed]

When we study any physical system we use differential element to get an equation then integrate over specific period to get a general form. Why we don't get directly a general form without ...
-1
votes
1answer
65 views

What does $f(v)d^3v$ mean?

I am reading the derivation of Langmuir's Evaporation Equation. The author writes: That cylinder contains a volume $dA(vdt)cosθ$ and contains vapor molecules of the designated speed in the ...
0
votes
1answer
38 views

How to treat the units of measure when taking a derivative?

I've had a doubt for a long time: when I'm taking the derivative, of a function for example, how should I treat the units of measurement? For example, if I'm taking the derivative of: $$S\,[{\rm m}]=...
15
votes
3answers
885 views

Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
0
votes
4answers
89 views

Explain $\Delta x = v_0t + \tfrac{1}{2}gt^2$ please? [duplicate]

$g = \Delta v/t$, so $\Delta v = gt$. $v = v_0 + \Delta v$, so $v = v_0 + gt$. So if $\Delta x = vt$, then $\Delta x$ should be $v_0t + gt$. Why the $\tfrac{1}{2}gt^2$? I'm really confused, so this ...
1
vote
4answers
56 views

Area under and slope of the motion graphs

I wanted to ask in general what area under the graph means. Also which physical quantity is highlighted by area under distance vs time graph. I'm confused that area is a 2 dimensional concept and it ...
4
votes
2answers
586 views

Check dimensions of the integral of a function

I and a colleague are arguing about the dimensions of: $$\int_0^x f(x) dx $$ in this particular case $[f(x)]=m^2/s^3$ and $[x]=m$. Does it follow that $[\int_0^x f(x) dx]=m^2/s^3$ or $[\int_0^x f(x)...
0
votes
1answer
105 views

Bridges between maths and physics: the $\tau=2\pi$ constant [closed]

[disclaimer: I am not a math or a CS major, this is probably an easy question for most people on Physics SE.] I just read the tau manifesto explaining - according to its author - the various ...
1
vote
1answer
51 views

Inverse metric in Newtonian limit of GR

I am reading Carroll's book. So looking at the Newtonian limit we write $g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$ where $h_{\mu\nu}$ is some small perturbation. He says that because $g^{\mu\nu}g_{\nu\...
0
votes
0answers
23 views

Spivak for a soon to be undergrad. physics student [duplicate]

I'll soon start my undergrad. studies in physics and because of that I picked up Spivak's Calculus a while ago to get a solid foundation in single-variable calculus before I start my studies. However, ...
0
votes
0answers
45 views

Difference between integral and differential physical laws [duplicate]

Why is integral and differential physical laws both used? I read that integral is global and differential is local. Could you tell me something about it?
0
votes
1answer
67 views

Use of infinitesimals in physics [duplicate]

I want to ask about infinitesimals and non-standard analysis. In physics we always use $\mathrm dx,~\mathrm dv,~\mathrm dt$ etc. as infinitesimal quantities. When we deduce equations in physics, when ...
0
votes
1answer
46 views

Vector Integrals: can I take out the vector outside of the integral?

Question: Solution: The notation used is: $(x,y,z)$ is for rectangular coordinates, $(\rho,\varphi,z)$ for cylindrical coordinates and $(r,\theta,\varphi)$ for spherical coordinates. ${ { \hat ...
0
votes
1answer
27 views

Equations of motion acceleration doubt

So i was going through some text today morning. Where it said $$ a = \frac{vdv}{dx} $$ So they then went on to, $$ vdv = adx \\ \implies \int vdv = \int adx$$ But,I am very certain acceleration is ...
1
vote
3answers
47 views

Equations of motion derivation doubt

I just started on learning how to derive the equations of motion using calculus. This is my first time and I have a basic doubt. So $v = \large{\frac{dx}{dt}}$ Then, $dx = v dt $ What does this ...
1
vote
0answers
38 views

Finding the exponent of $\lambda$ in Wien's displacement law

I am reading this paper on a short history of the $T^4$ radiation law. In particular, on page 5, By assuming that the wavelength of radiation emitted by a molecule was a function only of its ...
2
votes
0answers
69 views

What is the variation of pressure in rotating fluids(in accordance to the question in the image)? [closed]

This is an interesting question that I came across. Please see attachment. It is a multiple answer type question. My answer was B and D. I have attached my derivation for this problem. I want to know ...
5
votes
3answers
939 views

What are the differences between the differential and integral forms of (e.g. Maxwell's) equations?

I would like to understand what has to be differential and integral form of the same function, for example the famous equations of James Clerk Maxwell: How to know where to apply each way? Excuse ...
4
votes
3answers
218 views

Is $\dfrac{dx}{dt}$ a fraction or not?

I am new to calculus and during my mathematics class my sir defined $\dfrac{dx}{dt}$ as $$dx/dt=\lim_{t\to t_1}\dfrac{f(t)-f(t_1)}{t-t_1}$$ and my sir made a clear statement that $\dfrac{dx}{dt}$ ...
0
votes
1answer
37 views

Differential Operator

I am trying to understand the following expression \begin{eqnarray} e^{-ik.x}D_{\mu}D^{\mu}e^{ik.x} & = & e^{-ik.x}(i\partial_{\mu}+A_{\mu})(i\partial^{\mu}+A^{\mu})e^{ik.x}\\ & = & e^{...
0
votes
2answers
79 views

Is the motion of a particle non-analytic?

I really can't understand what happens during the time $t(0)$ to $t(0+dt)$ in the following crackpot arguement: A particle is at rest (in an ideal frictionless world) until $t(0)$. So every order ...
8
votes
5answers
41k views

How to get distance when acceleration is not constant?

I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question. The equation for distance of an accelerating object with constant ...
0
votes
0answers
33 views

How to derive velocity, distance from a changing acceleration?

I'm making a electronic device that is out of the scope of this site, but essentially it gives me acceleration readings every X microseconds. Given these samples of acceleration, how can I find out ...
0
votes
3answers
42 views

Flux - Scalar Multiplication in Integral?

No textbook and website seems to answer this so here is my question: When we have a scalar flux: I understand that you take the scalar product of the vectors. And I understand the need for using an ...
0
votes
3answers
78 views

A relationship between entropy and temperature

I tried deriving a formula relating entropy (not change in entropy, but entropy itself) to temperature. I’ve only seen two equations really relating to entropy thus far, and only one of them includes ...
8
votes
2answers
842 views

Three integrals in Peskin's Textbook

Peskin's QFT textbook 1.page 14 $$\int_0 ^\infty \mathrm{d}p\ p \sin px \ e^{-it\sqrt{p^2 +m^2}}$$ when $x^2\gg t^2$, how do I apply the method of stationary phase to get the book's answer. 2....
1
vote
1answer
39 views

Quick question - infinitesimals proofs [duplicate]

In a few of my courses in mechanics certain statements/equations have been proved by assuming that two infinitesimals multiplied by each other are zero. For instance in the equation : $dx + dy + dx^2 ...
2
votes
1answer
52 views

Satellite and gravitational acceleration

According to $0.5gt^2$ object will fall 5m in first second. Earth curve is 5m for 8km So if we can project object at 8000 m/s speed object will never fall into ground. Above scenario is correct ...
1
vote
0answers
25 views

Help to verify (numerically) invariant Haar measure on unitary group

Sorry if this question is not appropriate for the forum. From the paper http://gemma.ujf.cas.cz/~brauner/files/Haar_measure.pdf I am interested to understand and verify equation (3). Can anyone please ...
1
vote
1answer
98 views

What is the meaning of $\mathrm{d}^4k$ in this integral?

From Gerardus 't Hooft's Nobel Lecture, December 8, 1999, he states the following equation (2.1): $$ \int \mathrm{d}^4k \frac{\operatorname{Pol}(k_{\mu})}{(k^2+m^2)\bigl((k+q)^2+m^2\bigr)} = \infty ...
0
votes
1answer
56 views

If the integral is zero when is the integrand zero? [closed]

Using Stoke's theorem we prove that the curl of the Electric field vanishes. This would be possible only if the integrand is zero when the integral is zero.
0
votes
1answer
92 views

Fallacious derivation of the rocket equation

Consider a rocket in free space of initial mass (including fuel) of $m_0$ using up/ejecting fuel at a constant rate $r$ (mass per time). That means that at time $t$ the rocket has mass $m=m_0-rt$. The ...
0
votes
1answer
91 views

Does the complex conjugate of a vector have the same direction as the vector?

Looking at reflected and transmitted optic waves, the $\overset{\rightharpoonup }{E}_t$ vector is always perpendicular to $\overset{\rightharpoonup }{k}_t$ (as seen in the attached image). So $\...
0
votes
1answer
74 views

Calculating Potential Energy

I'm familiar with the potential energy equation, but I'm concerned with the value of 'g' in it. I know that, at sea level, earth's gravitational acceleration is 9.81 m/s/s. So I know that within the ...
0
votes
1answer
39 views

The dot product integral in the proof of the Parallel axis theorem

The first picture is a question about proving the Parallel axis theorem and the second is the solution. I have no problem with the solution except for the part which says that $$ \int 2\vec h \cdot \...
0
votes
1answer
47 views

Differential derivation based upon time and space confusion

I have been doing a lot of derivations recently involving heat transfer. I was attempting to derive heat accumulation in a differential element based upon inflow and outflow as well as thermodynamic ...
1
vote
0answers
40 views

3 Particle problem with a difference

Please read this completely, it is not the typical question you expect. 3 particles are at the corners of an equilateral triangle with side a. Assume that particle 1 is at (0,0), particle 2 is at (a,...
2
votes
2answers
59 views

Why dont you take derivative of force in definition of power ? P=F.v

The derivative of work is $\bf F\cdot v .$ $$P(t)= \frac{\mathrm dW}{\mathrm dt}= \mathbf{F\cdot v}=-\frac{\mathrm dU}{\mathrm dt}\;.$$ But why not $$(\mathrm d(\mathbf F)/\mathrm dx)\cdot \mathbf x ...
1
vote
0answers
28 views

Is there a way to find the optimal angle to launch an object to get maximum distance when there is an initial height? (Projectile motion) [duplicate]

I know that the optimal angle to launch an object at ground level is 45 degrees; however, i want to know that if there is anyway to get the optimal angle to launch an object to get the maximum ...
1
vote
1answer
119 views

What does $L^2(S^1,\mu_H)$ mean?

It's a Hilbert space, $\mu_H$ stands for the Haar measure on $U(1)$, but what does $S^1$ mean? I found it in one of my quantum mechanics books which approaches from a very 'mathematical' way.
1
vote
1answer
37 views

How to model terminal velocity as a function of gravitational acceleration?

Taking the most simplistic form of terminal velocity, $v=\sqrt{\frac{mg}{c}}$ I want to try and derive an equation that models the velocity as g changes in height.. Because obviously the terminal ...
0
votes
2answers
87 views

Derivation of a kinematical equation [duplicate]

My question is, we can calculate distance of free falling objects with the equation of $d = \frac{1}{2}gt^2$ where $d$ is distance in meter, $t$ is time in seconds, but I wonder how we achieved this ...
48
votes
7answers
3k views

How to treat differentials and infinitesimals?

In my Calculus class, my math teacher said that differentials such as $dx$ are not numbers, and should not be treated as such. In my physics class, it seems like we treat differentials exactly like ...