Step 1: Understanding the Concept:
A particle moving in a circle with a constant angular speed is undergoing uniform circular motion. In this type of motion, the magnitude of velocity (speed) is constant, but the direction of velocity changes continuously.
Step 2: Key Formula or Approach:
In uniform circular motion:
1. The velocity vector $\vec{v}$ is always directed along the tangent to the circular path at any point.
2. The acceleration is purely centripetal, meaning it arises solely from the change in direction of velocity. The formula for centripetal acceleration magnitude is $a_c = \frac{v^2}{r}$, and its direction is always radially inward towards the center of the circle.
Step 3: Detailed Explanation:
Let's evaluate each statement:
(A) "The velocity vector is tangent to the circle." - This is true for any circular motion.
(C) "The velocity and acceleration vectors are perpendicular to each other." - Since velocity is tangential and acceleration is radial (pointing to the center), they are indeed perpendicular ($90^\circ$ to each other). This is true.
(D) "The acceleration vector points to the centre of the circle." - This describes centripetal acceleration, which is correct for uniform circular motion. This is true.
(B) "The acceleration vector is tangent to the circle." - Tangential acceleration only exists if the particle's speed (or angular speed) is changing. Since the angular speed is constant, the tangential acceleration is zero. The net acceleration is purely radial. Thus, this statement is false.
Step 4: Final Answer:
The false statement is that the acceleration vector is tangent to the circle.