A curved treadmill having a base comprises: an exercise surface configured for rotating around a first roller and a second roller, converting the potential energy of the user on the exercise surface into rotational kinetic energy; a first pulley operatively connected to the first roller adapted to rotate around a respective rotation axis. The base comprises a first coupling device of the first pulley with the first roller operatively connected between the first roller and the first pulley. The first coupling device, during the rotation of the physical exercise surface in a first rotation sense along the longitudinal axis of the base, allows rotation of the first pulley and the first roller around the respective rotation axis if the rotation speed of the first roller is equal to or greater than the rotation speed of the first pulley, and prevents rotation of the first pulley and the first roller around the respective rotation axis if the rotation speed of the first roller is lower than the rotation speed of the first pulley. Thus users can perform different physical exercises.