Rest tremor (RT) is observed in subjects with Parkinson's disease (PD) and Essential Tremor (ET). Electromyography (EMG) studies have shown that PD subjects exhibit alternating contractions of antagonistic muscles involved in tremors, while the contraction pattern of antagonistic muscles is synchronous in ET subjects. Therefore, the RT pattern can be used as a potential biomarker for differentiating PD from ET subjects. In this study, we developed a new wearable device and method for differentiating alternating from a synchronous RT pattern using inertial data. The novelty of our approach relies on the fact that the evaluation of synchronous or alternating tremor patterns using inertial sensors has never been described so far, and current approaches to evaluate the tremor patterns are based on surface EMG, which may be difficult to carry out for non-specialized operators. This new device, named "RT-Ring", is based on a six-axis inertial measurement unit and a Bluetooth Low-Energy microprocessor, and can be worn on a finger of the tremulous hand. A mobile app guides the operator through the whole acquisition process of inertial data from the hand with RT, and the prediction of tremor patterns is performed on a remote server through machine learning (ML) models. We used two decision tree-based algorithms, XGBoost and Random Forest, which were trained on features extracted from inertial data and achieved a classification accuracy of 92% and 89%, respectively, in differentiating alternating from synchronous tremor segments in the validation set. Finally, the classification response (alternating or synchronous RT pattern) is shown to the operator on the mobile app within a few seconds. This study is the first to demonstrate that different electromyographic tremor patterns have their counterparts in terms of rhythmic movement features, thus making inertial data suitable for predicting the muscular contraction pattern of tremors.