Teams of flying robots can be used for inspection, delivery, and construction tasks, in which they might be required to fly very close to each other. In such close-proximity cases, nonlinear aerodynamic effects can cause catastrophic crashes, necessitating each robots' awareness of the surrounding. Existing approaches rely on multiple, expensive or heavy perception sensors. Such perception methods are impractical to use on nano multirotors that are constrained with respect to weight, computation, and price. Instead, we propose to use the often ignored yaw degree-of-freedom of multirotors to spin a single, cheap and lightweight monocular camera at a high angular rate for omnidirectional awareness of the neighboring robots. We provide a dataset collected with real-world physical flights as well as with 3D-rendered scenes and compare two existing learning-based methods in different settings with respect to success rate, relative position estimation, and downwash prediction accuracy. We demonstrate that our proposed spinning camera is capable of predicting the presence of aerodynamic downwash with an $F_1$ score of over 80% in a challenging swapping task.