Why does a boomerang come back?

Unlike an airplane or helicopter propeller, which starts spinning while the vehicle is completely still, you throw a boomerang. It does more than just spin around its axis. It flies through the air.

Refer to the diagram below. At some instant in time we see that whichever wing is at the top of the spin is moving in the same direction as the forward motion of the throw. Simultaneously, the wing is at the bottom of the spin is moving in the opposite direction. This means that while both wings are spinning at the same speed, the top wing is actually moving through the air at a faster speed than the bottom wing.

When a wing moves through the air more quickly, the Bernoulli effect produces a larger aerodynamic lift. Unlike a helicopter rotor, the lift acts mainly sideways on the boomerang instead of upward. This aerodynamic force imbalance is noted in the diagram.

If the boomerang were not spinning, the unbalanced push at the top would make it tip. Nevertheless, it is torque and angular momentum that we deal with when we have a spinning object, just the way it works for a top or a gyroscope.

Since the aerodynamic lift points along the same direction as the spin axis of the boomerang, the resulting torque acts at a right angle to the boomerang's spin axis. This changes the direction of the boomerang's axis without really changing its rotation speed. As the torque turns the spin axis, the flight path of the boomerang turns along with it. The shifting of the spin axis along the boomerang flight path is shown in the diagram below.