Many research social studies of public response on social media require following (i.e., tracking) topics on Twitter for long periods of time. The current approaches rely on streaming tweets based on some hashtags or keywords, or following some Twitter accounts. Such approaches lead to limited coverage of on-topic tweets. In this paper, we introduce a novel technique for following such topics in a more effective way. A topic is defined as a set of well-prepared queries that cover the static side of the topic. We propose an automatic approach that adapts to emerging aspects of a tracked broad topic over time. We tested our tracking approach on three broad dynamic topics that are hot in different categories: Egyptian politics, Syrian conflict, and international sports. We measured the effectiveness of our approach over four full days spanning a period of four months to ensure consistency in effectiveness. Experimental results showed that, on average, our approach achieved over 100% increase in recall relative to the baseline Boolean approach, while maintaining an acceptable precision of 83%.