If a particle moves in a circle describing equal angles in equal intervals of time, then the velocity vector.

Options

A. changes its magnitude only
B. changes its direction only
C. changes both its magnitude and direction
D. both magnitude and direction remains constant

Answer

To solve the problem, we need to analyze the motion of a particle moving in a circle while describing equal angles in equal intervals of time. Let's break down the steps:

### Step-by-Step Solution:

1. **Understanding the Motion**:
- The particle is moving in a circular path and is described to cover equal angles in equal time intervals. This indicates uniform angular motion.

2. **Defining Angular Velocity**:
- The angular displacement (θ) is constant for each time interval (t). Therefore, the angular velocity (ω) can be defined as:
\[ \omega = \frac{d\theta}{dt} \]
- Since both \(d\theta\) and \(dt\) are constant, it follows that ω is constant.

3. **Relating Linear Velocity to Angular Velocity**:
- The linear velocity (v) of the particle moving in a circle can be expressed in terms of the radius (r) and angular velocity (ω):
\[ v = r \cdot \omega \]
- Since the radius (r) is constant for circular motion and ω is constant (as established), the linear velocity (v) is also constant in magnitude.

4. **Direction of the Velocity Vector**:
- Although the magnitude of the velocity is constant, the direction of the velocity vector changes continuously as the particle moves along the circular path. The velocity vector is always tangent to the circle at the particle's position.

5. **Conclusion**:
- Therefore, while the magnitude of the velocity remains constant, the direction of the velocity vector changes continuously as the particle moves in a circle.

### Final Answer:
The velocity vector changes in direction only, while its magnitude remains constant.

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