The following photos will give an idea how to build a comparable mobile but you will have to use your own scrounged gear so I won't go into real specifics.
Step 1: Make an Airplane, Attach Motor and Boom
The following website provides some really neat planes that can be made from cardboard in black and white and color. I chose the Spitfire.
Attach the motor to the plane. I used a cable tie to do that.
Find a toy propeller from one of those broken airplanes we all seem to have and attach to motor shaft. I drilled a shaft size hole in my propeller and attached with super glue.
Then you must attach the plane to a boom approximately 4 feel long and of any kind of material.
I used a piece of hollow fishing pole. Again I used zip cables to attach the plane to the boom.
Run the two wires from the motor inside the boom (or outside if you wish).
Step 2: Attach Counterweight to Boom
Tape or zip ties.
Step 3: Make Support Wire With Fishing Snap Swivels
Attach one end of the wire to a fishing snap swivel. The other end will be attached to the boom using a zip tie.
If you are not using a solar cell or a transformer for power then you can simply attach a battery to the motor wires with a switch and you are basically finished. Hang the mobile, balance it so the plane is level, turn on the switch and away it goes.
The only problem with a battery is that the power will go down in a matter of minutes.
One solution is to use a solar cell like I did so follow the additional steps to create a way to get the power from an external source to the airplane. Simply attaching a power source to the motor wires will not work because as the mobile turns it will wrap the wires together and stall.
Step 4: Making a Rotating Power Connection (aka Slip Ring)
The second power line is provided by attaching a washer to the support line with a nylon or wood spacer.
Solder a wire to the bottom of this washer and run the other end of the line to the boom and one of the motor wires.
Now solder a wire to a nut. This nut will spin freely on top of the washer. Run the wire from the nut to one of the solar cell
connections. The second photo shows the bottom of the support wire is attached to one of the motor wires.
Run the other solar cell wire to the support wire - I attached mine with an alligator clamp. At the other end of the support wire, attach that end to the other motor wire.
Step 5: Connect Power Supply (solar Cell or Transformer)
As I learned, if you are using a solar cell, you cannot use fluorescent lighting, it must be incandescent.
Mount your solar cell near the light source but not so close you heat the solar cell up and ruin it.
(WARNING: Incandescent bulbs are hot and dangerous. During a test I melted a solar cell when it came in contact with the bulb. Many years ago I sat some clothing next to a bulb and then left my apartment. For some reason I came back early to find my apartment full of smoke and a shirt on fire. I shudder to think what would of happened if I had not come back early.
Anyway, this solar cell solution is not a permanent fix for me and I will be converting the power source to a low voltage transformer or power supply.) Test the solar cell with your finger, if it is too hot to keep your finger on it then it is too hot to be safe.
Update: 11/23 - I converted this mobile from solar cell to use a 5 volt transformer with a pot to get the voltage down to about two volts. The solar cell was erratic in performance. The pot allows me to control the speed of the motor and how fast the mobile will rotate - it can go very fast if I want. See second photo that shows transformer plugged into the light socket and the little black box hanging down which is the pot control. The pot came out of a broken servo.
Step 6: Hang Mobile, Connect Power Supply
Enjoy your airplane!