Can a moving object have a constant speed but a changing velocity?

Write the equation for centripetal acceleration in uniform circular motion. Obtain these equations in terms of angular velocity $(\omega)$ and frequency $(\nu)$.

The position vector of a particle is $\vec{r} = (a \cos \omega t)\hat{i} + (a \sin \omega t)\hat{j}$. The velocity of the particle is

$A$ merry-go-round rotating at a constant angular speed completes $9$ rotations in $18$ seconds. What is its angular speed?

If a body is moving in a circle of radius $r$ with a constant speed $v$,its angular velocity is:

$A$ particle $P$ is moving in a circle of radius $a$ with a uniform speed $v$. $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$,the angular velocity of $P$ about $A$ and $C$ are in the ratio: