The situation in which the normal component of acceleration is zero and the tangential component is non-zero occurs when an object moves in a circular path at a constant speed. This implies that the object is experiencing centripetal acceleration, directed toward the center of the circle, while its speed remains unchanged.
Let's consider an example to illustrate this situation. Imagine a car traveling on a racetrack in a perfectly circular path. The car maintains a constant speed throughout the entire motion.
In this scenario, the car's acceleration can be broken down into two components: the normal (or radial) component and the tangential component.
The normal component of acceleration (an) is directed perpendicular to the motion of the car, towards the center of the circular path. It is responsible for continuously changing the direction of the car's velocity vector.
At any point on the racetrack, the car's velocity vector points tangent to the circle. The tangential component of acceleration (at) is parallel to the velocity vector and is responsible for changing the car's speed (magnitude of velocity) while keeping it moving in a circular path.
Since the car is moving at a constant speed, the tangential component of acceleration (at) is non-zero because it is responsible for maintaining the car's velocity. However, the normal component of acceleration (an) is zero because the car's speed remains constant, and there is no acceleration directed toward or away from the center of the circle.
The balance between the centripetal force (provided by friction between the car's tires and the racetrack) and the car's inertia allows for the car to move in a circular path while maintaining a constant speed.
In summary, situations where the normal component of acceleration is zero and the tangential component is non-zero occur when an object moves in a circular path at a constant speed. The centripetal acceleration (tangential component) keeps the object on the circular path, while the object's speed remains unchanged.