Explanation:

When a particle moves with constant speed in a circle, it undergoes circular motion. The direction of velocity changes continuously and the magnitude of velocity remains constant.

What is average velocity?

Average velocity is the displacement of an object divided by the time taken. It is a vector quantity and has both magnitude and direction.

What happens after half rotation?

After half rotation, the direction of velocity changes by 180 degrees and the displacement is equal to the diameter of the circle. The time taken for half rotation is equal to half the time period of the circular motion.

How to calculate average velocity after half rotation?

To calculate the average velocity after half rotation, we need to find the displacement and time taken.

- Displacement: The displacement after half rotation is equal to the diameter of the circle, which is 2r, where r is the radius of the circle.
- Time taken: The time taken for half rotation is equal to half the time period of the circular motion, which is T/2, where T is the time period of the circular motion.

Therefore, the average velocity after half rotation is:

v_avg = 2r / (T/2) = 4r/T

This formula shows that the magnitude of average velocity after half rotation is equal to twice the magnitude of the velocity divided by the time period of the circular motion.

Conclusion:

In conclusion, when a particle moves with constant speed in a circle, the magnitude of average velocity after half rotation is equal to twice the magnitude of the velocity divided by the time period of the circular motion. This formula is derived from the displacement and time taken for half rotation.