If a particle moves in a circle describing equal angles in equal times, its velocity vector

To understand the behavior of the velocity vector of the particle, let us analyze its motion step-by-step:

1. Understanding Uniform Circular Motion:
The question states that a particle moves in a circle and describes equal angles in equal times. This means that the angular speed ($\omega$) of the particle is constant. Since the radius ($r$) of the circular path is constant, the linear speed ($v$), which is given by the relation:
$v=r\omega$
must also remain constant. Therefore, the magnitude of the velocity (speed) remains constant.

2. Analyzing the Velocity Vector:
Velocity is a vector quantity, which has both magnitude and direction. For any object moving in a circular path, the direction of the velocity vector at any point is always tangent to the circle at that point.

3. Direction Changes Continuously:
As the particle moves along the circular perimeter, the direction of the tangent changes continuously at every single point. Even though the magnitude of the velocity (its speed) is constant, the continuous change in the orientation of the tangent means that the velocity vector is constantly changing its direction.

Therefore, the velocity vector of the particle changes in direction.