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The purpose of this study was to examine the accuracy of methods to estimate ball spin rate and spin axis direction using multi-camera tracking technology. The method implemented by Hawk-Eye and a theoretical ball trajectory model were assessed for their accuracy against high speed-vision. A theoretical ball trajectory model was found to estimate ball spin rate and the spin axis direction more accurately than the method used by Hawk-Eye. The superior performance of the ball trajectory model was indicated by a lower mean bias and standard deviation (2.92 ± 222.76) than Hawk-Eye (−100.01 ± 542.44), as well as narrower limits of agreement and a 327.63 RPM lower RMSE. Spin rates less than 4500 RPM were estimated with the highest accuracy, but neither method was able to consistently and accurately estimate spin rates >4500 RPM. The application of a trajectory model to multi-camera ball tracking data provides a practical and non-invasive method to accurately estimate the spin imparted when hitting, allowing for large-scale collection of spin rates during matches. [ABSTRACT FROM AUTHOR]

The article discusses the study titled "Impulse and work for the bullet-block Veritasium video," by C. E. Mungan which noted the conversion of translational energy into gravitational potential energy. It states that gravitational potential energy can be converted from translational energy when an object is projected vertically as rotational energy cannot be converted in this manner. Particular focus is also given to the correlation between rolling friction and ball diameter.

The objective of this paper is to use data from the highest level in men's tennis to assess whether there is any evidence to reject the hypothesis that the two players in a match have a constant probability of winning each set in the match. The data consists of all 4883 matches of grand slam men's singles over a 10 year period from 1995 to 2004. Each match is categorised by its sequence of win (W) or loss (L) (in set 1, set 2, set 3,...) to the eventual winner. Thus, there are several categories of matches from WWW to LLWWW. The methodology involves fitting several probabilistic models to the frequencies of the above ten categories. One four-set category is observed to occur significantly more often than the other two. Correspondingly, a couple of the five-set categories occur more frequently than the others. This pattern is consistent when the data is split into two five-year subsets. The data provides significant statistical evidence that the probability of winning a set within a match varies from set to set. The data supports the conclusion that, at the highest level of men's singles tennis, the better player (not necessarily the winner) lifts his play in certain situations at least some of the time. Key PointsUsing grand slam men's singles data, the probability of winning a set has been shown to vary from set to set.The data provides statistical evidence that the better player (not necessarily the winner) in some matches is able to lift his play in certain situations. This result gives encouragement to the better player when in difficulties in a match.The authors found no evidence that the weaker player was able to lift his play. The weaker player, when ahead in a match, should be on his guard for his opponent to have a real capacity to lift his game.