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(C) Statement $A$ is true: In uniform circular motion,the acceleration $\vec{a}$ is purely centripetal,directed towards the center. The velocity $\vec

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$A$ is true but $B$ is false

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(C) Statement $A$ is true: In uniform circular motion,the acceleration $\vec{a}$ is purely centripetal,directed towards the center. The velocity $\vec{v}$ is tangential to the path. The angular velocity $\vec{\omega}$ is perpendicular to the plane of the circle. Thus,$\vec{\omega}$,$\vec{v}$,and $\vec{a}$ are mutually perpendicular.Statement $B$ is false: In non-uniform circular motion,the acceleration $\vec{a}$ has both a centripetal component $\vec{a}_c$ and a tangential component $\vec{a}_t$. The net acceleration $\vec{a} = \vec{a}_c + \vec{a}_t$ is not perpendicular to the velocity $\vec{v}$ because $\vec{a}_t$ is parallel to $\vec{v}$. Therefore,they are not mutually perpendicular.

Consider the two statements related to circular motion in usual notations:
$A$. In uniform circular motion,$\vec{\omega}$,$\vec{v}$,and $\vec{a}$ are always mutually perpendicular.
$B$. In non-uniform circular motion,$\vec{\omega}$,$\vec{v}$,and $\vec{a}$ are always mutually perpendicular.

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Consider the two statements related to circular motion in usual notations:$A$. In uniform circular motion,$\vec{\omega}$,$\vec{v}$,and $\vec{a}$ are always mutually perpendicular.$B$. In non-uniform circular motion,$\vec{\omega}$,$\vec{v}$,and $\vec{a}$ are always mutually perpendicular.