Question $7-8$ points

A $4$ kg object and a $2$ kg object are suspended and joined by a pulley with radius $7$ cm and mass $1\mathrm{.}3$ kg $.$ The pulley experiences a frictional torque of $0\mathrm{.}50N*m.$ The masses start from rest.

$($a$)$ Determine the final speed of the $4\mathrm{.}0$ kg object as it hits the ground.

$($b$)$ Determine the tangential acceleration of the pulley

$($c$)$ Knowing that $=d\frac{}{d}t$ and that acceleration is constant, determine the equation for angular velocity of the pulley.