Human physical motion activity identification has many potential applications in various fields, such as medical diagnosis, military sensing, sports analysis, and human-computer security interaction. With the recent advances in smartphones and wearable technologies, it has become common for such devices to have embedded motion sensors that are able to sense even small body movements. This study collected human activity data from 60 participants across two different days for a total of six activities recorded by gyroscope and accelerometer sensors in a modern smartphone. The paper investigates to what extent different activities can be identified by utilising machine learning algorithms using approaches such as majority algorithmic voting. More analyses are also provided that reveal which time and frequency domain based features were best able to identify individuals motion activity types. Overall, the proposed approach achieved a classification accuracy of 98 percent in identifying four different activities: walking, walking upstairs, walking downstairs, and sitting while the subject is calm and doing a typical desk-based activity.