Recent content by Andrew Mason

If ##a^0\ne 1## then ##a^0\ne -e^{\pi i}## and the beauty of mathematics would be gone. AM

Hmmm. So those green craters on the pizza at the bottom of my fridge could be due to radioactivity?! I thought it was just the usual mold and other fridge grunge: AM

There are other threads that discuss the similarities and differences between thermodynamic entropy Boltzmann entropy and Clausius entropy, and Shannon entropy: https://www.physicsforums.com/threads/shannon-entropy-and-origins-of-the-universe.733843/...

The radius of Jupiter at the equator is 71,500 km and the radius of Io’s orbit is 422,000 km. The radius of Jupiter’s orbit about the Sun is 5.2 AU. So the drawing is very misleading. In order to see Io enter Jupiter’s shadow and then emerge you would have to be viewing it from the side. One...

Whether Earth is moving toward or away from Jupiter is almost immaterial in itself. The orbital period of Io is about 42.5 hours. In that time the maximum possible change in distance between Earth and Jupiter is 15 light seconds. If the Earth is moving toward Jupiter at time t, it will be...

As Berkeman has pointed out you would need to cancel the marble’s orbital speed first in order for the marble to drop vertically to the Earth surface. The orbital speed is about 3066 m/s given by ##v=\sqrt{\frac{GM}{r}}## where r=42,164 km. So it has to lose a lot of velocity make it drop...

If the thermodynamic work done by the gas changes the polarization of the gas molecules, that would be taken into account in the change in electrical energy of the capacitor. Polarization energy would have to change the degrees of freedom or heat capacity of the gas molecules since ##\Delta...

How can you determine the gas polarization energy if you aren’t given any information about the polar nature of the gas molecules? AM

You have found an easier way to solve the problem by noticing that ##a=3/2=\gamma##, the adiabatic constant (Cp=3R;Cv=2R). So the process is equivalent to an adiabatic process:->Q=0. The work done by the gas in increasing the separation of the plates is stored as electrical potential energy of...

The use of capital V for volume and voltage is confusing. I will use lower case ##v## for voltage and upper case ##V## for volume. Your result for ##a=1.5## looks right. Since ##PV^a=\text{constant}=P_0V_0^a## and ##P=nRT/V## then ##nRTV^{a-1}=nRT_0V_0^{a-1}## so...

Just so I am clear on the linkage, the angle of BD to the extension of BC is a fixed 120° and B is free to slide along BC. You are being asked then to find the linear velocity of D and angular velocity of BD when the angle of AB to the extension of AC is 60°. The angular velocity of AB is a...

.... Wade is a journalist and has developed his own 'theories' about race and genetics. He has come under a lot of criticism for his most recent book (2014), A Troublesome Inheritance: Genes, Race, and Human History. Here is a rather uncharitable review of that book and Wade's approach...

This graphic from the paper published in Nature in 2015 may help explain the data that Reich was using: The green bars represent the proportion of genes in the populations in the stated country or region added from migrants from the steppe regions of eastern Europe and Asia (Yamnaya); The...

So 3 times the fundamental is a harmonic (a twelfth) but not 1.5 (fifth). You might find musicians who would disagree that a perfect fifth is not a harmonic interval. AM

The OP was using "overtones" to refer to the sequential harmonics above the fundamental tone. I was just doing the same. I don't think there is a hard an fast rule relating musical terms (overtones) and physics terms (harmonics). AM