A large grinding wheel in the shape of a solid cylinder of radius $0\mathrm{.}330$ m is free to rotate on a frictionless, vertical axle. A constant tangential force of $230$ N applied to its edge causes the wheel to have an angular acceleration of $0\mathrm{.}866$ rad$/$s$2.$

$($a$)$ What is the moment of inertia of the wheel?

kg $$ m$2$

$($b$)$ What is the mass of the wheel?

kg

$($c$)$ If the wheel starts from rest, what is its angular velocity after $5\mathrm{.}70$ s have elapsed, assuming the force is acting during that time?

rad$/$s