Problem — The boomerang that returns

Problem

Explain the physical principle by which a correctly thrown boomerang returns to the thrower. Use the concepts of asymmetric lift and precession.

Solution

The boomerang is thrown nearly vertically and spins rapidly about itself, with a large angular momentum $\vec{L}$ along its rotation axis. Its two blades have the profile of a wing.

Because of the rotation, the blade that at a given instant is moving forward (in the direction of flight) meets the air at a higher relative speed than the blade moving backward. The faster blade generates more lift: this creates a lift asymmetry between the top and bottom of the disc of rotation.

This unbalanced lift produces a torque $\vec{\tau}$ perpendicular to $\vec{L}$. By the law $\dfrac{d\vec{L}}{dt} = \vec{\tau}$, the boomerang’s axis precesses slowly, progressively curving the trajectory into a wide circle that brings it back to the thrower. $\ev{\text{asymmetric lift} \Rightarrow \vec\tau\perp\vec L \Rightarrow \text{precession} \Rightarrow \text{circular return trajectory}}$

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Topics: Rotational dynamics Concepts: Angular momentum · Torque