15.8 : Relative Motion Analysis using Rotating Axes

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.

However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it instrumental in understanding the relative position. The velocity of point B is then calculated as a vector sum of the absolute velocity of point A and the relative rotational velocity of point B with respect to point A. The relative velocity of point B is made up of two terms.

The first term represents the velocity components of point B, but relative to the rotating frame of reference. The second term, on the other hand, signifies the rate of change of the unit vectors of the rotating frame. This can be expressed in terms of angular velocity.

Therefore, in conclusion, the absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame. This comprehensive approach allows for a more accurate and nuanced understanding of the movements within the system.