Angular acceleration $\alpha$ is the rate of change of angular velocity: $\alpha =\frac{d\omega }{dt}$. Linear tangential velocity is $v=r\omega$. Tangential acceleration $a_t$ is the rate of change of $v$: $a_t=\frac{dv}{dt}=\frac{d(r\omega )}{dt}=r\frac{d\omega }{dt}=r\alpha$. This relationship is only for the component of acceleration along the path tangent; there is also a radial (centripetal) acceleration $a_c=v^2/r=r{\omega }^2$.