Displacement after half a circle in a circular path

Introduction:
When a particle moves in a circular path of radius r, its displacement after half a circle can be determined using various concepts such as distance, displacement, and angle.

Key concepts:
To understand the displacement after half a circle, we need to consider the following key concepts:
- Distance: The total length of the path traveled by the particle.
- Displacement: The change in position of the particle from its initial position to its final position.
- Angle: The angle subtended by the arc of the circular path.

Displacement and distance:
- Displacement is a vector quantity that represents the change in position of an object. It has both magnitude and direction.
- Distance, on the other hand, is a scalar quantity that represents the total length of the path traveled by an object. It only has magnitude.

Half a circle:
- A circle is a complete 360-degree revolution, so half a circle is equal to 180 degrees.
- When a particle completes half a circle, it returns to its starting position, resulting in a displacement of zero.
- However, the distance traveled by the particle would be equal to the circumference of half a circle, which can be calculated using the formula C = 2πr, where r is the radius of the circle.

Calculating the displacement after half a circle:
To calculate the displacement after half a circle, we can use the following steps:

Step 1: Determine the angle subtended by the arc of the circular path.
- In this case, the angle is 180 degrees.

Step 2: Use the formula to calculate the displacement.
- Displacement = 2πr (θ/360), where θ is the angle in degrees and r is the radius of the circle.
- Displacement = 2πr (180/360)
- Displacement = 2πr/2
- Displacement = πr

Conclusion:
After half a circle in a circular path of radius r, the displacement of the particle is equal to πr. This means that the particle moves a distance equal to the radius of the circle in the opposite direction from its initial position. It is important to note that the displacement is a vector quantity, while the distance is a scalar quantity.