Reliable health monitoring of mechanical components in aerial robotic systems is crucial to their safe operation. The highly constrained nature of aerial systems requires that such systems operate with a minimum of sensing and computational power. This article proposes a method for the detection and diagnosis of motor/propeller degradation on a multicopter aerial robot. The proposed method works by monitoring the accelerometer output, and effectively correlates vibration power to the motor commands, allowing it to estimate the magnitude of a propeller's unbalance mass. This is done directly in the time domain with a recursive implementation. The method makes low computational and memory demands, and relies only on the accelerometer almost universally present on aerial robots, so that it may be easily implemented on existing platforms as well as new designs. Experiments show reliable detection of a faulty propeller on three distinct multicopter platforms: two quadcopters whose masses differ by more than an order of magnitude, and a hexacopter; one vehicle has brushed motors, two have brushless motors. The proposed method requires only a minimum of assumptions about the vehicle's dynamic model, and does not, e.g., require knowledge of the vehicle's center of mass or its mass moment of inertia.