Question

A particle starting from the rest moves with a constant angular acceleration alpha in a circular path the time a t which magnitude of tangential and radial acceleration are equal

Answer 1

Angular acceleration = alpha

let 't' be the time at which the magnitude of tangential and radial acceleration are equal so, A/c to question

tangential acceleration = radial acceleration

r×alpha =v^2/r

or, v=r (alpha)^1/2

or, omega× r = r (alpha) ^1/2

or, theta/t = (alpha)^1/2

or, t = theta/ ( alpha)^1/2

hence,

theta/ ( alpha)^1/2 is the required time when both are equal.

Hope it helps you...