How to detect angular position of a device mounted on a rotating wheel?
There are a number of options. A few include:


Capacitive sensor - detects ground coming and going and allows a maximum to be detected.
As the ground is at a fixed angle to the wheel support structure, detecting when a point goes past a swing arm or fork or whatever will allow you to determine when another point is near the ground.
Sensor can then be inductive, magnetic etc.
Optical sensor can detect ground proximity - either passive using daylight or by detecting eg an infrared beam.
Simple RADAR  can do this well enough - this can be as simple as a few transistors.
Acoustic (usually ultrasonic) position detection can do this.
Magnetic detector determines wheel position using earth's magnetic field OR field of an attached magnet.   
Hall sensor, fluxgate and similar measure field strength.
GMR. AMR and similar measure field angle.
Two (or 3) orthogonal coils can detect position in space relative to a field. 
Gyroscope (Mems)


More ...

Tell us what you REALLY want to do and we'll tell you how to do it :-).

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Accelerometer:

Steven has mentioned accelerometer. I thought of this but left it out. These are relatively cheap and are readily available. But if this is on a vehicle (and that wheel is turning at a considerable speed for a vehicle if it is a normal wheel size) then accelerations due to turning and acceleration in various planes will make the job harder. You will still get a cyclic gravity variation of +/- 1g but it will be added to centripetal acceleration and turning, suspension and impact force effects. It MAY be the best solution, but some other that is not so affected by the vehicle dynamics is liable to be better. 



RADAR

A Doppler RADAR may be implemented by using a self oscillating  transistor or push pull pair at VHY  or UHF to mix return signal with outgoing signal and return the difference frequency, which is the Doppler signal. The oscillator needs to be short term stable enough for the Doppler frequency difference to be detectable but can be less stable long term. 

Here's a curcuit from someone pushing this to the limit. That's from US patent 4672379 - no guarantee of practicality as shown. I recall a hobby magazine in the last 20 years or so doing a self oscillating psuhpull pair with perhaps a diode detector. And Silicon Chip magazine (13 November 2006) published a RADAR speed gun project. 



Here's a RADAR operated lamp circuit !
 VT1 oscillates and receives. C couples the low frequency Doppler difference signal to amplifiers A1, buffered by A2, magic by A3 and rectified by  A2 A3 then it is rectified by 





Here is an excellent assembly manual for Ramsey SG7 personal speed radar which does NOT have a circuit diagram but provides enough visual detail of the RF board for the very simple circuit of the RF transceiver and mixer to be easily traced out. Viz - 





It would be nice not to have to play "guess 1000 questions" and just have the real spec explained instead of sneaking up on it slowly, as we are doing now. If this is for a "hub odometer" type arrangement whose main aim is to measure wheel RPM then an easy and effective way is to have an internal "bob weight" which hangs down internally and does not rotate when the wheel does. The electronics then sense it going past a point on the PCB etc. This needs a mechanical bearing but this is very easy to do, easy to design and can be very long life indeed. The hub-odometer industry churns these out by the millions. This is THE easiest high output level simple arrangement if you can tolerate the bearing requirement. 

People have made electronic rotation sensing hubodometers for decades. Many of the methods mentioned by me and others could be made to work. A cyclical waveform that changes within cerain rate boundarioes can be extracted from the noise. eg an accelerometer can be arranged to be orthogonal (at 90 degrees) to "centrifugal" acceleration and will see cyclical gravity variation. Radar should be easy enough [tm] Note it may want to see wheel arches etc depending on where it is pointed. 

You MAY be able to do a differential capacitance sensor - or inductance. With two sensing "ends" at 180 degrees one will see road while other is seeing sky so signal will vary between two states with A-B at one monet and B-A 180 degres later. Even very low level signals can be extracted by autocorrelation or other means.