A discus thrower accelerates a discus from rest to a speed of $25\mathrm{.}3$ m$/$s by whirling it through $1\mathrm{.}26$ rev. Assume the discus moves on the arc of a circle $1\mathrm{.}05$ 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.

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 $25\mathrm{.}3$ m$/$s$.$

s