13.2:
Equations of Motion: Normal and Tangetial Components
The motion of a particle in a curvilinear path can be described using the normal and tangential components.
The normal component is directed along the normal (or radial) path to the curve at a particular point. It depicts the variation in the trajectory of the velocity vector.
The tangential component is tangential to the curve at a specific point and characterizes the rate at which speed changes along the path.
The equation of motion for a particle in a curvilinear motion can be expressed using Newton's second law of motion along normal and tangential components.
Here, positive tangential acceleration represents an increase in the magnitude of the speed, and negative tangential acceleration represents a decrease in the magnitude of the speed of the particle.
On the other hand, the normal component of the acceleration is always along the radius of the curved path, and it is positive when directed towards the center of the curvature. The normal component of the force is also defined as centripetal force.
13.2:
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.