tangential vs angular acceleration

Question

Tangential acceleration a_t relates to angular acceleration α by:

RankGuru · Accepted Answer

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 $a_c = v^2/r = r \omega^2$.

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tangential vs angular acceleration

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