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### TAMU Physics Festival and Rotating Discs in Special Relativity

The Texas A&M Physics Department Physics Festival is today[5]!!!  If you're in town, you should wonder over to the Mitchell Physics building, (see the picture), on University Drive.  Nobel laureates will speak, there will be three showings of a physics circus, and there will be tens and possible over a hundred hands on demos to take a look at.  Lately, the chemistry, mathematics, and engineering departments have gotten in on the fun, so things could get crazy!  Oh, and there's almost certainly going to be exploding bottles of liquid nitrogen used to erupt water out of barrels, a perennial crowd pleaser.

On the theory side of things this week, I'm working on re-calculating the line element of the Takeno transform.  The transform was derived by Takeno in 1952 in an attempt to explain what happens to a rotating disc when it rotates at special relativistic speeds.  There's been a conundrum here almost since the inception of special relativity in 1905.  It was pointed out that if length contracts in the direction tangential to travel, (along the circumference of the disc in this case), and it doesn't contract in directions at right angles to travel, then the circumference of the disc would grow smaller while the radius of the disc would be unchanged and the formula for the circumference, C=2*Pi*r would no longer hold.  The issue has never  been resolved to everyone's satisfaction nd there's still a lively debate in the journals[2][3][4].

References:
1.  Takeno H. “On Relativistic Theory of Rotating Disk”, Prog. Theor. Phys. 7, (1952), 367

2.  Spatial geometry of the rotating disk and its non-rotating counterpart

3.  On rotation and rotating frames: Franklin transformation and its modiﬁcation

4.  New Perspectives on the Relativistically Rotating Disk and Non-time-orthogonal Reference Frames

5.  Physics Festival

### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

### Lost Phone

We were incredibly lucky to have both been in university settings when our kids were born.  When No. 1 arrived, we were both still grad students.  Not long after No. 2 arrived, (about 10 days to be exact), mom-person defended her dissertation and gained the appellation prependage Dr.

While there are lots of perks attendant to grad school, not the least of them phenomenal health insurance, that’s not the one that’s come to mind for me just now.  The one I’m most grateful for at the moment with respect to our kids was the opportunities for sheer independence.  Most days, we’d meet for lunch on the quad of whatever university we were hanging out at at the time, (physics research requires a bit of travel), to eat lunch.  During those lunches, the kids could crawl, toddle, or jog off into the distance.  There were no roads, and therefore no cars.  And, I realize now with a certain wistful bliss I had no knowledge of at the time, there were also very few people at hand that new what a baby…

### Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…