29

In English, it seems that: Position is a vector. Distance/length is a name of its magnitude. Velocity is a vector. Speed is a name of its magnitude. Acceleration is a name of a vector and its magnitude. Force is a name of a vector and its magnitude. Momentum is a name of a vector and its magnitude. ... Velocity/speed as well as position/length seem to be ...


8

I think it’s just called a solenoidal field (incompressible field), because by definition, if we have $\mathbf{\nabla}\times \mathbf{A}= \mathbf{V}$, $$\mathbf{\nabla}\cdot(\mathbf{\nabla}\times\mathbf{A})= \mathbf{\nabla}\cdot \mathbf{V }=0$$ because the divergence of the curl is 0. Because of this, any field that can be derived from a vector potential is ...


6

It means to say that the difference, when $dx$ is infinitesimally small (in the sense of calculus), is proportional to $dx$ to the power 1, $dx^1$. For example, a Taylor expansion of a function near to a given point $x$, $$f(x + dx) = f(x) +dx f'(x) + \frac{1}{2} dx^2 f''(x) +...$$ Consists of an infinite number of terms that express the function with ...


5

In the general case -- i.e in any number of dimensions, the analogue of $\nabla\times(\nabla \phi)=0$ and $\nabla\cdot(\nabla\times {\bf A})=0$ is $d^2=0$ where $d$ is the exterior derivative anding on $p$-forms. This means that if $\omega=d\eta$ then $d\omega=0$. A p-form $\omega$ such that $d\omega=0$ is said to be closed. If $\omega= d\eta$ then $\omega$ ...


5

g-force is typically used to express the magnitude only, but the words are generally used interchangeably; laymen typically referring to the magnitude only.


3

A force of 5 N to the left is the same thing as a force of -5 N to the right. Born is just choosing, when there are two forces opposing each other to say they are both pointing to the right but one is negative, rather than to say one is to the right and the other is to the left. It doesn't change any of the physics, it's just a choice about how you ...


3

Assuming that the car is going at a constant speed, you can determine the impulse delivered to the car which is given by: $$\vec{F}_\text{avg} t = \Delta \vec{p}$$ While the magnitude of momentum will be constant, the direction will change. There are two locations in the motion that we can look at. Firstly, we need to look at the moment when the wheel ...


3

If the change in magnetic field can be neglected, it is called electrostatics. In this case, you can define an electric potential $V$: $$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} = 0 \Rightarrow \mathbf{E} = - \nabla V$$ If the change in the electric field and electric current can be neglected, it is called magnetostatics. In this ...


2

$$ C_{v} = \frac{3 k_B N}{2}$$ where $N$ is the number of atoms. Divide both sides by $N$ and we have $atom^{-1}$ on the LHS.


2

If you need a word, coin it, define it in your writing and use it consistently. I would use hastening or quickening. For instance, an object going around in a circle at constant speed (thus angular velocity) isn't quickening, though it is constantly accelerating.


2

“Phase” isn’t particularly well defined for non-sinusoidal waveforms. But we still use the language because we’re used to thinking of complicated waveforms as being made up of multiple sinusoidal components of different frequencies. In that case, when you apply anti phase to each of those components separately, you get the inverse you’re looking for.


2

The name "antigravity" perks up people's interest more people than "artificial gravity", because antigravity suggests a way of getting off the planet, while artificial gravity is mainly useful once you're in space, and can already be simulated in spaceflight (for a human payload) with a simple centrifuge. The "propulsion" aspect applies even off-planet ...


1

The key point is that you want $$ \ddot{x}=-\frac{k}{m} x $$ for any constant $k$ since the solution to this is $x(t)=A\cos(\sqrt{\frac{k}{m}}\, t+\varphi)$ with $\varphi$ and $A$ obtained from the initial conditions. Thus the choice $k=m\omega_0^2$ $$ m\ddot{x}=-\omega_0^2 m x $$ allows you to eliminate $m$ cleanly and be left with $\sqrt{k/m}=\omega_0$,...


1

However, I don't entirely grasp the physical meaning of conservative fields, I thought understanding where the label came from might help me understand what it is that we're describing. It may be helpful to think in terms of the conservative forces associated with conservative fields, like the gravitational and electromagnetic forces. A conservative ...


1

Neither. Like @pobably_someone I have never heard the term "thermic" in connection with "temperature". According to Wikipedia the term thermic was once used for "thermodynamics", and sometimes refers to an "exothermic" or "endothermic" process. The term "thermal" is a term to avoid since it is frequently used as an adjective for energy ("thermal energy"). ...


1

When one studies mathematics, one knows that a mathematical theory starts from axioms and then mathematics is used to prove theorems. When axioms change, the theory changes. A good example is Euclidean Geometry versus spherical geometry. Also in mathematics, a theorem may be used as an axiom, and the original axiom proven as a theorem. Physics theories use ...


1

As pointed out by Safesphere, the physical laws that rule the world are expressed at a higher and more general level of (mathematical) abstraction which underlie Newton's laws. We can then derive Newton's laws from them as needed to solve everyday problems in real-world dynamics. These more general relationships are generically called symmetries; if you ...


1

If the domain is topologically trivial, then, as explained in the other answers, "is a curl" is the same as "incompressible," i.e., has zero divergence. So that's your answer. In examples like the electric field of a point charge, the domain has a hole in it. This breaks the equivalence between incompressibility and is-a-curl. However, you asked this on a ...


1

In my opinion, both questions are provoked by translation problems. Concerning your question 1: In the original german version it reads “gleichgerichtet” which rather means same “alignment ” than same “direction”. Concerning question 2: in the original, Born does not refer to any experiment but exactly to the Gedanken experiment he describes in the ...


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