Distance and Placement of a Particle on a Circle
The movement of a particle along a circle of radius r can be analyzed by considering its distance and placement during different parts of its revolution. Let's explore the distance and placement of the particle in half of its revolution.

Distance of Particle
- The distance covered by the particle in half of its revolution can be calculated using the formula for the circumference of a circle: C = 2πr.
- In half of a revolution, the particle travels half of the circumference of the circle, which is equal to half of 2πr = πr.
- Therefore, the distance covered by the particle in half of its revolution is πr.

Placement of Particle
- As the particle moves along the circle, its placement can be determined by the angle it has covered in relation to the center of the circle.
- In half of its revolution, the particle has covered an angle of 180 degrees (π radians).
- The placement of the particle in half of its revolution is at a point on the circle that is exactly opposite to its initial position.
- This means that the particle is located on the diametrically opposite side of the circle from where it started.
In conclusion, in half of its revolution, the particle on a circle of radius r covers a distance of πr and is located at a point diametrically opposite to its initial position. Understanding the distance and placement of the particle in different parts of its revolution can help in analyzing its motion and trajectory along the circle.