For physical activity recognition, smartphone sensors, such as an accelerometer and a gyroscope, are being utilized in many research studies. So far, particularly, the accelerometer has been extensively studied. In a few recent studies, a combination of a gyroscope, a magnetometer (in a supporting role) and an accelerometer (in a lead role) has been used with the aim to improve the recognition performance. How and when are various motion sensors, which are available on a smartphone, best used for better recognition performance, either individually or in combination? This is yet to be explored. In order to investigate this question, in this paper, we explore how these various motion sensors behave in different situations in the activity recognition process. For this purpose, we designed a data collection experiment where ten participants performed seven different activities carrying smart phones at different positions. Based on the analysis of this data set, we show that these sensors, except the magnetometer, are each capable of taking the lead roles individually, depending on the type of activity being recognized, the body position, the used data features and the classification method employed (personalized or generalized). We also show that their combination only improves the overall recognition performance when their individual performances are not very high, so that there is room for performance improvement. We have made our data set and our data collection application publicly available, thereby making our experiments reproducible.