Which of the following statements is FALSE for a paricle moving in a circle with a constant angular sppeed?

Options

A. The acceleration vector points to the centre of the circle
B. The acceleration vector is tangent to the circle
C. The velocity vector is tangent to the circle
D. The velocity and acceleration vectors are perpendicular to each other

Explanation

To determine which statement is FALSE for a particle moving in a circle with a constant angular speed, we need to analyze the properties of circular motion. Let's go through the statements step by step.

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A particle moving in a circle with constant angular speed means that it maintains a steady rate of rotation around the center of the circle.
- The angular speed (ω) is constant, which implies that the linear speed (v) is also constant because \( v = \omega r \), where r is the radius of the circle.

2. **Acceleration in Circular Motion**:
- In uniform circular motion, the acceleration is directed towards the center of the circle (centripetal acceleration). This is necessary to keep the particle moving in a circular path.
- Therefore, the statement that "the acceleration vector points to the center of the circle" is TRUE.

3. **Tangential Acceleration**:
- Since the speed is constant, there is no change in the magnitude of the velocity, which means there is no tangential acceleration.
- Thus, the statement that "the acceleration vector is tangent to the circle" is FALSE because the acceleration is directed towards the center, not tangentially.

4. **Velocity Vector**:
- The velocity vector of a particle in circular motion is always tangent to the circle at any point. This is TRUE.

5. **Perpendicularity of Velocity and Acceleration**:
- The velocity vector (tangent to the circle) and the acceleration vector (pointing towards the center) are perpendicular to each other. This is also TRUE.

6. **Conclusion**:
- The only statement that is FALSE is that "the acceleration vector is tangent to the circle".

### Final Answer:
The FALSE statement for a particle moving in a circle with constant angular speed is: **"The acceleration vector is tangent to the circle."**

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