### Motors!!!

One of the kids' friends asked about magnets a few weeks ago.  This led to three weeks worth of play dates on electric circuits, electromagnets, and last but not least, Motors!!!  (It's nice to have a physicist in the family).

The motors were amazingly simple to put together, so I’m including the instructions.  Here’s a picture so we have something to talk about.

The parts are:
1 D cell battery
1 pound of 18 awg magnet wire, (you don’t need the whole pound, but Amazon sells It by the pound… seriously)
1 piece of cardboard out of the side of a box,
1 magnet
scotch tape

The How
Tape the D cell to the cardboard so it can’t move.  Next, cut two 4 inch pieces of magnet wire.  The next step is a bit of work, but use a kitchen knife, or a piece of sandpaper to scrape off the red insulation until you just see bare copper wire.  Place a dime size loop in one end of the wire, and then bend it over at a right angle to the rest of the wire to serve as a foot.  In the other end of the wire, make at least two pencil diameter loops to hold up the motor’s rotor, (the large coil of wire shown in the picture).  Tape the feet you made to the cardboard on either side of the battery, then tape the two wires to either side of the battery so that each of them is in contact with one of the poles, (the silver ends), of the battery.  Wrap the tape around a few times, and wrap it tight to make sure each wire is actually touching the pole.

Next, wrap magnet wire around the D cell to make the rotor coil.  Make about 10 turns.  This coil of wire is going to be the motor’s rotor, (a fancy name for the spinning bit).  Tie the ends of the wire through the loop so the loop can’t unravel, and leave about two inches of wire sticking out from opposite sides of the loop as shown in the picture.

Here’s the tricky bit.  Strip half the insulation off the pieces of wire sticking out from the coil.  Make the ends of the wire look like the diagram below.

If you strip off all the insulation, the motor won’t work.  The wire extending from the rotor needs to make electrical contact with the pencil diameter wire hoops attached to the battery only half the time.  It’ll spin through half a circle making electrical contact to the two posts you made earlier, and then during the next half circle it won’t.  Watch the wire on the left side of the rotor in the video . As it spins, you'll see that the side with insulation is visible, and then the side with bare metal.  (More on this in the ‘Why It Works’ section).

Now, insert the rotor into the pencil diameter hoops as shown in the picture.  Place the magnet on the battery pointed up at the rotor.  Then, give the rotor a little spin to get it moving, and it should spin happily around all on its own.

Next Time: Why it works

All the stuff for making motors:

### 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…

### 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…

### Unschooling Math Jams: Squaring Numbers in their own Base

Some of the most fun I have working on math with seven year-old No. 1 is discovering new things about math myself.  Last week, we discovered that square of any number in its own base is 100!  Pretty cool!  As usual we figured it out by talking rather than by writing things down, and as usual it was sheer happenstance that we figured it out at all.  Here’s how it went.

I've really been looking forward to working through multiplication ala binary numbers with seven year-old No. 1.  She kind of beat me to the punch though: in the last few weeks she's been learning her multiplication tables in base 10 on her own.  This became apparent when five year-old No. 2 decided he wanted to do some 'schoolwork' a few days back.

"I can sing that song... about the letters? all by myself now!"  2 meant the alphabet song.  His attitude towards academics is the ultimate in not retaining unnecessary facts, not even the name of the song :)

After 2 had worked his way through the so…