An old grindstone, used for sharpening tools, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is $0\mathrm{.}330$ m$.$ A constant tangential force of $300$ N applied to its edge causes the wheel to have an angular acceleration of $0\mathrm{.}844$ rad$/$s$2.$

$($a$)$

What is the moment of inertia of the wheel $($in kg $$ m$2)?$

kg $$ m$2$

$($b$)$

What is the mass $($in kg$)$ of the wheel?

kg

$($c$)$

The wheel starts from rest and the tangential force remains constant over a time period of $4\mathrm{.}50$ s$.$ What is the angular speed $($in rad$/$s$)$ of the wheel at the end of this time period?

rad$/$s