"$A$ particle moving with constant speed on a circle about a fixed axis has a constant angular velocity,but its linear velocity is not constant." Is this possible? Why?

(A) Yes,this is possible. In uniform circular motion,the magnitude of the linear velocity (speed) remains constant,but the direction of the linear velocity vector changes continuously at every point along the circular path. Since velocity is a vector quantity,a change in direction implies a change in velocity. On the other hand,the angular velocity $\omega$ is defined as $\omega = \frac{d\theta}{dt}$. For a particle moving with constant speed $v$ in a circle of radius $r$,the angular velocity is $\omega = \frac{v}{r}$. Since both $v$ and $r$ are constant,the angular velocity $\omega$ remains constant in both magnitude and direction (along the axis of rotation).