In this paper we introduce the design of a light-weight novel flexible-joint arm for light-weight unmanned aerial vehicles (UAVs), which can be used both for safe physical interaction with the environment and it represents also a preliminary step in the direction of performing quick motions for tasks such as hammering or throwing. The actuator consists of an active pulley driven by a rotational servo motor, a passive pulley which is attached to a rigid link, and the elastic connections (springs) between these two pulleys. We identify the physical parameters of the system, and use an optimal control strategy to maximize its velocity by taking advantage of elastic components. The prototype can be extended to a light-weight variable stiffness actuator. The flexible-joint arm is applied on a quadrotor, to be used in aerial physical interaction tasks, which implies that the elastic components can also be used for stable interaction absorbing the interactive disturbances which might damage the flying system and its hardware. The design is validated through several experiments, and future developments are discussed in the paper.