A discus thrower accelerates a discus from rest to a speed of $24\mathrm{.}6$ m$/$s by whirling it through $1\mathrm{.}29$ rev. Assume the discus moves on the arc of a circle $1\mathrm{.}01$ m in radius.

A discus thrower moving in a circle as he prepares to throw the discus.

$($a$)$ Calculate the final angular speed of the discus.

What is the relationship between the angular velocity and the linear speed of a point on the edge of the circle? rad$/$s

$($b$)$ Determine the magnitude of the angular acceleration of the discus, assuming it to be constant.

rad$/$s$2$

$($c$)$ Calculate the time interval required for the discus to accelerate from rest to $24\mathrm{.}6$ m$/$s$.$