Is the tangential acceleration of a particle moving in a circular path always zero? Under what condition is it zero?

(N/A) No,the tangential acceleration is not always zero. The tangential acceleration $a_t$ is defined as the rate of change of the magnitude of velocity,given by $a_t = \frac{dv}{dt} = r \alpha$,where $r$ is the radius and $\alpha$ is the angular acceleration.
If the particle moves with a constant speed (uniform circular motion),then $\frac{dv}{dt} = 0$,which implies $a_t = 0$.
If the particle moves with a variable speed (non-uniform circular motion),then $\alpha \neq 0$,and the tangential acceleration is non-zero.