Abstract: The present invention is directed to a winding apparatus and method for winding a thread on a golf ball center. The apparatus comprises a plurality of rotating members supported for rotation and guiding the thread to a golf ball center winding station. The sum of the rotational inertias of the rotating members is low or less than about 3000 grams-cm2. The apparatus further includes a roller and at least one brake operatively connected with the roller for changing the rotation thereof. The brake can be a magnetic brake and include a permanent magnet or an electro-magnet. The method of the present invention allows the tension to be changed by applying a magnetic force to at least one roller. In one embodiment, the step of changing the tension includes using a magnetic brake. The present invention is particularly useful in winding thread with a breaking tension below about 800 grams.