Equations of Motion: Normal and Tangetial Components

The normal component is directed along the radial path to the curve and depicts how the trajectory of the velocity vector changes. The tangential component is tangential to the curve and characterizes the rate at which speed changes along the path. Together, they fully describe particle motion in curvilinear paths using Newton's second law.

Positive tangential acceleration increases the magnitude of the particle's speed along the path, while negative tangential acceleration decreases it. The tangential component of force directly controls whether the particle speeds up or slows down as it moves along the curved trajectory.

The normal component of acceleration always aligns with the radius of the curved path and is positive when directed toward the center of curvature. This component changes the direction of the velocity vector without altering the particle's speed, enabling the curved trajectory.

The normal component of force is identified as centripetal force because it acts radially inward toward the center of curvature, continuously pulling the particle toward the center. This inward-directed force is essential for maintaining the particle's curved path and preventing it from moving in a straight line.

Newton's second law of motion is employed to express the equation of motion for particles undergoing curvilinear motion by resolving forces and accelerations into normal and tangential components. This approach allows engineers to analyze how both speed and direction change simultaneously along a curved path.

Positive normal acceleration indicates that the acceleration vector is directed toward the center of curvature along the radial direction. This inward acceleration is necessary to change the particle's direction and maintain its motion along the curved path. It represents the centripetal acceleration required for circular or curved motion.

Examine the sign of the tangential acceleration component. If tangential acceleration is positive, the particle is speeding up; if negative, it is slowing down. The normal acceleration component, meanwhile, only changes the particle's direction, not its speed magnitude along the path.