# Tag Info

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Ultimately, Newton's law of cooling is a simplification that can be obtained from the full heat equation, i.e. $$\rho c\frac{\partial T}{\partial t} = - \kappa \nabla \cdot T.$$ The heat equation itself can be derived from first principles, assuming Fourier's law for heat flow, namely that it is proportional microscopically to the difference in temperature ...

0

How do we know that the rate at which a body loses heat is proportional to the difference between its temperature and that of its environment? In classical physics this is a law. "Fourier's law The law of heat conduction, also known as Fourier's law, states that the time rate of heat transfer through a material is proportional to the negative ...

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It appears Newton himself did some experimentation, but failed to divulge exactly what he did - though he said "he used a linseed oil thermometer" and the resulting data. Source: History of Newton's Law of Cooling

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In a sense this is an assumption, however it's an assumption that has a basis in the history of QM at the time. I attach images of four pages from http://www.amazon.com/Einstein-Quantum-Quest-Valiant-Swabian/dp/0691168563, which I'm currently reading and recommend if you're interested in the history, that give something of the flavor. Bohr can be said to ...

1

To give a qualitative answer, the equivalence of gravitational and inertial mass is not a coincidence. Mass has inertia and this resists its motion through space-time (we're moving into the future at the speed of light!). The resistance leads to a bending of space-time and it is this that we interpret as gravity. Sort of...

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Pulsar has already given a correct answer. In this answer we will use a slightly different (but equivalent) method, and we will keep a watchful eye on possible distributional contributions. George Green uses Gaussian units where Coulomb's constant $k_e=1$. He is considering a ball with radius $a$ and uniform charge density $\rho_0$, i.e. of total charge ...

2

Let you apply force $\bf F$ at point $P$ the coordinate of which is $\bf r$ measured from a specific point $O$ - the point about which you want to rotate. Let $\bf r$ and $\bf F$ be in the same plane. Now, if you were to rotate $P$ about $O$, it would rotate around some axis perpendicular to the plane in which the force and the point lies; if ...

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Let's first derive the value of $V$ inside the small sphere: $$V_\text{sphe} = \rho\int\frac{\text{d}x'\text{d}y'\text{d}z'}{r'},$$ Where the sphere is sufficiently small such that $\rho$ can be considered constant. We can orientate the axes such that $p$ lies on the $z'$ axis. In spherical coordinates, the integral then has the form  \begin{align} ...

2

Bohr's atom became famous for reproducing the Rydberg formula for spectral lines of hydrogen, which Rydberg presented in 1888 and published the next year. Bohr remarked that it was Rydberg's switching from wavelengths to wavenumbers that allowed him to make the discovery. His inspiration came from Balmer's 1885 formula, which was a particular case, and had ...

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A good starting point would be the series of papers by Bohr, starting with "On the constitution of atoms and molecules" Philos. Mag. 26, 1 (1913) and checking the references therein.

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Tyco Brahe Observed Mars. And as the Mars is out side us, and rotates slower, it has an particular character that it even moves to "wrong direction" in the sky for a while. It must have been partially luck, that 5 of these observations is measures with enough accuracy this important point in orbit. (see link) Or maybe this was exactly the interesting ...

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They couldn't carry sufficently accurate time from London with portable clocks. But they were able to use clocks to time measure the time between the sun crossing and the transit of stars the night before and after. The absolute transit time of stars can be trivially obtained if you know the site's longitude. If you are on land and have an observatory ...

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For short periods of time very accurate time could be kept by using pendulums.

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The second paragraph from this IEEE reference follows: Every electrical engineer learns early of the two Kirchhoff laws, but not very many realize that they were published while he was still a student. The publication is {(vom Studiosus) Kirchhoff, “Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesonere durch eine kreisförmige,” ...

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