The tag has no usage guidance.

learn more… | top users | synonyms

1
vote
0answers
26 views

Fourier Transform point force on a half-space [migrated]

I have to calculate the following Inverse Fourier-Transform, which describe the potential function for a point force on a half-space: ...
0
votes
2answers
64 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 ...
0
votes
0answers
31 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
27 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
63 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 ...
7
votes
2answers
750 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. ...
1
vote
1answer
34 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
47 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
19 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
95 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
49 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
84 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
80 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
53 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
34 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 ...
0
votes
1answer
45 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
37 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 ...
2
votes
2answers
57 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
116 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
83 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 ...
47
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 ...
13
votes
2answers
829 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
0answers
12 views

Calculate distance with variable acceleration [duplicate]

I know the time and I know the force that acts horizontally on a particle. The problem is that the force is F=k(D-V), where k and D are constants. So at the beginning where the particle has zero ...
0
votes
3answers
308 views

How to prove the average velocity formula without calculus

I often see the formula: $$ \overline v = \frac {v + v_0}{2} $$ in physics textbooks, to describe the average velocity for an object moving with constant acceleration. This formula is often ...
1
vote
0answers
47 views

Calculus/Vector Calculus and so on in special relativity book recommandation

I want to learn calculus 1,2,3 vector calculus, analysis and so on in special relativity. But I never found a good and clear book/source on it. Can someone recommend an easy book or internet source on ...
1
vote
2answers
76 views

Divergence-free vector field on a non-simply connected domain

We know that divergence-free vector fields are themselves curls of vector fields on simply connected domains. I want to construct a counterexample in the case the domain is not simply connected. So ...
7
votes
6answers
888 views

Is Newton's first law something real or a mathematical formalism?

Why do objects always 'tend' to move in straight lines? How come, everytime I see a curved path that an object takes, I can always say that the object tends to move in a straight line over 'small' ...
0
votes
2answers
135 views

Calculus versus Algebraic Kinematic Equations

Deriving the first equation of motion using either algebra or calculus you get the exact same thing, but my knowledge was that you use integral calculus in physics when you have a varying variable, ...
5
votes
1answer
197 views

Optimization of Bottle Rocket Water Level

My (entry-level) physics class is building bottle rockets, and we are competing to build the longest-flying bottle rocket. The rockets are filled partway (we get to decide how much to fill them) with ...
1
vote
0answers
51 views

When a coil makes a complete turn, why is does magnetic flux double with respect to time?

EMF, $\mathcal{E}$, is equal to -d($\phi$)/dt Where $\phi$ is magnetic flux. Why is it that if from $t_1$ to $t_2$ the coil makes a complete turn and during this turn the normal vector's angle with ...
0
votes
0answers
32 views

Why does the angular average of the divergence result in a factor 1/3?

In going from eq.(6.13) to (6.14) in http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf it is assumed that ...
0
votes
1answer
50 views

How do you interpret definite-integrating of both sides of an equation?

Consider a particle is moving at an acceleration of $a=f(s)$ [$s$ stands for particle's location) if we have the initial velocity of a particle then what is the final velocity? So... we know that ...
0
votes
2answers
183 views

Can you take the integral of $ d^2x\over dt^2$? [closed]

I am messing around with physics problems, and as silly as this maybe how do you take the integral of $$\int_0^\infty xd^2x$$ For example taking Newton's Second law $F=ma$ $$ F=m{d^2x\over dt^2} ...
1
vote
0answers
41 views

Why is the angular average of the direction of the momentum squared a third instead of one?

In the article http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf (in going from eq. (6.13) to eq. (6.14)) it is stated that ...
0
votes
2answers
143 views

Work done against gravity comes out positive

Given two points in 3-space, $A = (9, 1, 5)$ and $B=(2,8,7)$, the work done by the gravitational field $\bf{F}$ when an object is moved from point $A$ to point $B$ comes out positive, even though it ...
0
votes
2answers
43 views

Faraday's law and potential along a closed curve

$$\int(\nabla \times \vec{E}) \cdot d\vec{S} = \oint \vec{E}\cdot d\vec{l} = -\frac{\mathrm{d} \phi_b}{\mathrm{d} t}$$ The second expression is the potential difference along a closed curve. Isn't ...
1
vote
0answers
72 views

Is $d^3r$ the same as $dV$, the volume element?

I've seen the term $d^3r$ being used instead of $dV$. Are they exactly the same? Do they have a different connotation?
1
vote
1answer
55 views

Derive an equation related to magnetism [closed]

Solve the equations for $v_x$ and $v_y$ : $$m\frac{d({v_x)}}{dt} = qv_yB \qquad m\frac{d{(v_y)}}{dt} = -qv_xB$$ by differentiating them with respect to time to obtain two equations of the ...
5
votes
4answers
6k views

Divergence of $\frac{\hat{r}}{r^2}$

In David J. Griffiths's Introduction to Electrodynamics, the author gave the following problem in an exercise. Sketch the vector function $$ \vec{v} ~=~ \frac{\hat{r}}{r^2}, $$ and compute ...
0
votes
1answer
28 views

Electric field uniform circle $R$ direction cancel out

I am doing a physics problem involving a uniform circle with a total charge of X, and am attempting to find the electric field on a point charge on the axis of the circle a distance of Z away. I ...
0
votes
1answer
54 views

Hermitian Conjugate in Spherical Coordinate System [duplicate]

Help me find $\hat{B^\dagger}$, when we know that $$\hat{B}=i\frac{d}{dr}$$ with the condition that $\hat{B}$ is defined in spherical coordinates. My approach: $$ ...
-1
votes
2answers
48 views

Find $\oint xdx+2ydy+3zdz$ on the line segment formed by points $A(1,0,-1)$,$B(2,5,-1)$ [closed]

Find $\oint xdx+2ydy+3zdz$ on the line segment formed by points $A(1,0,-1)$,$B(2,5,-1)$ My approach: First I find the line segment formed by $A,B$ which is $\vec ...
-4
votes
2answers
56 views

Do I need to differentiate this equation or not?

I've been given this equation: $$\mathrm{velocity}, v = 2\,\mathrm{cm/s^3} \,t^2 + 5\,\rm cm/s.$$ If someone now asks me to tell the velocity at, say 4 sec, then before proceeding with the equation, ...
1
vote
1answer
130 views

Derivation of Torricelli's equation

I am reading "Fundamentals of Physics" by Shanker and he is deriving Torricelli's equation. First he says $\displaystyle a = \frac{dv}{dt}$. Next, he multiplies both sides by velocity to get ...
0
votes
0answers
52 views

Little problem with surface integral

I've read a problem and I think there's a mistake in it. The problem is as follows. Note: The surface is the surface of a sphere. \begin{equation} \oint\frac{d\vec{a}}{d} \end{equation} Where ...
1
vote
2answers
80 views

Units of the derivative of a function

I have a function $\phi(\mu, \sigma)$. $\mu$ and $\sigma$ are voltages (in mV in my case), so $\phi$ is a function of two voltages. $\phi$ itself, however, is in units of time (ms in my case). ...
1
vote
2answers
89 views

Would condensed matter physicists need more than three dimensional calculus? [closed]

The difference between "multivariable" and "vector" calculus, as stated on Yale's website, is that multivariable would only go through 2 or 3 dimensions, and so would rely heavily on geometric ...
0
votes
0answers
75 views

Expanding Electric Field, Magnetic Field in post-Newtonian Gravitational Potential

I've cross-posted this question from Mathematics since Physics is probably better suited for the nature of the question. I've ...