A particle is executing uniform circular motion with velocity $\vec{v}$ and acceleration $\vec{a}$. Which of t

Question

A particle is executing uniform circular motion with velocity $\vec{v}$ and acceleration $\vec{a}$. Which of the following is true?

Accepted Answer

1.  **Analyze Velocity ($\vec{v}$):** In uniform circular motion, the speed (magnitude of velocity) remains constant. However, the direction of motion changes continuously at every point (tangential to the circular path). Since velocity is a vector quantity possessing both magnitude and direction, a change in direction means the velocity vector $\vec{v}$ is not constant .
2.  **Analyze Acceleration ($\vec{a}$):** The particle experiences centripetal acceleration directed towards the centre of the circle. The magnitude of this acceleration ($a_c = v^2/R$) is constant because $v$ and $R$ are constant. However, the direction of the acceleration vector changes continuously as the particle moves, always pointing towards the centre. Since the direction changes, the acceleration vector $\vec{a}$ is not constant .
3.  **Conclusion:** Both velocity and acceleration vectors change in direction continuously. Therefore, neither $\vec{v}$ nor $\vec{a}$ is a constant vector.

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