A boomerang has two wings that are shaped into airfoils so that they generate lift when it spins the way a propeller does. When it is thrown one wing will generate more lift than the other because the airflow over it is added to the airflow from it’s spin while the other has it subtracted. This uneven lift would tend tip the ‘rang over but because it is spinning another force comes into play that as I write this has yet to be mentioned; [gyroscopic precession](https://www.youtube.com/watch?v=mRZGdvJQnPU)
When the unequal lift attempts rotate the axis of spin of the ‘rang, precession turns it at a right angle causing the ‘rang to fly in a turning path. The higher the forward speed the greater the unequal lift the harder the turn. This result in a well made and well thrown ‘rang returning to the thrower and settling into a helicopter like descent to be caught.
A boomerang has two or more airfoil lifting surfaces. When you throw it, you spin it. That means the wing going forward generates a bit more lift than the wing going backwards because the air is flowing over the wing just a little bit faster. Because a boomerang is spinning, it behaves like a gyroscope. Gyroscopes are weird counterintuitive things. If you apply a turning force, a torque, to a gyroscope, where the axis of torque is at right angles to the axis the gyroscope is spinning, the result is the gyroscope axis shifts towards an axis that is at right angles to both the initial spinning axis and the axis of the applied torque. The torque generated by the differential lift causes the boomerang to therefore curve in flight and eventually come back to where you start. [This guy](http://www2.eng.cam.ac.uk/~hemh1/boomerangs.htm) has all the info you ever want to know about how boomerangs work.
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