The Displacement After Half a Circle

To determine the displacement of a particle after it has completed half a circle, we need to understand the concept of displacement and the properties of circular motion.

Displacement:
Displacement is a vector quantity that represents the change in position of an object from its initial position to its final position. It is defined as the shortest distance between the initial and final positions, taking into account both magnitude and direction.

Circular Motion:
Circular motion occurs when an object moves along a circular path. The path of the object is defined by its radius, and the object continuously changes its direction while maintaining a constant speed. The displacement of an object in circular motion is determined by the change in its position relative to its starting point.

Determining the Displacement:
When a particle moves in a circular path of radius r, its displacement after half a circle can be determined by considering the properties of circular motion.

1. Initial and Final Positions: Let's assume the particle starts at point A on the circular path and completes half a circle to reach point B. The initial position of the particle is at point A, and the final position is at point B.

2. Radius and Circumference: The radius of the circular path is represented by r. The circumference of the circle is given by the formula C = 2πr, where π is a mathematical constant approximately equal to 3.14159.

3. Distance Covered: Since the particle completes half a circle, it covers half the circumference of the circle. Therefore, the distance covered by the particle is equal to half the circumference, which can be calculated as D = 0.5 * C = 0.5 * 2πr = πr.

4. Displacement: The displacement of the particle is the shortest distance between the initial and final positions. In this case, as the particle moves along a circular path, the displacement is equal to the diameter of the circle, which is 2r.

Conclusion:
After half a circle, the displacement of a particle moving in a circular path of radius r is equal to 2r, which is the diameter of the circle. It is important to note that displacement is a vector quantity, meaning it has both magnitude and direction. In this case, the direction of the displacement would be from the initial position to the final position along the diameter of the circle.