Equations of Motion: Normal and Tangetial Components

Describing the motion of a particle along a curvilinear path involves understanding its components in terms of normal and tangential aspects. The normal component aligns with the radial direction of the curve at a specific point, reflecting changes in the trajectory of the velocity vector. In contrast, the tangential component is tangential to the curve at that point and signifies the rate at which speed alters along the path.

Newton's second law of motion is employed to articulate the equation of motion for a particle undergoing curvilinear motion, considering both normal and tangential components. Positive tangential acceleration indicates an increase in the magnitude of the speed, while negative tangential acceleration signifies a reduction in the particle's speed.

In this context, the normal component of acceleration always aligns with the radius of the curved path. When directed towards the center of curvature, it is considered positive. Furthermore, the normal component of force is identified as the centripetal force, establishing a crucial connection between the particle's dynamics and its curvilinear trajectory. This comprehensive approach facilitates a nuanced examination of particle motion within a curvilinear framework.