Answer
$a_{c}=\frac{v^{2}}{r}=\omega^{2}r$ and $a_{t}=r\times$ angular acceleration.
Change in $a_{t}$ means change in angular acceleration which implies change in $\omega$ hence change in $a_{c}$. So, centripetal acceleration must change, considering the radius to be constant.
Work Step by Step
$a_{c}=\frac{v^{2}}{r}=\omega^{2}r$ and $a_{t}=r\times$ angular acceleration.
Change in $a_{t}$ means change in angular acceleration which implies change in $\omega$ hence change in $a_{c}$. So, centripetal acceleration must change, considering the radius to be constant.