Torque on Baseball going through pitching machine

MechE1507

1. The problem statement, all variables and given/known data

I am designing a shaft for a pitching machine that uses a spinning tire to accelerate a ball and must determine the torque acting on the shaft when a ball goes through the machine. A 1/4 horsepower motor is spinning an 8 inch tire at 1900RPM, constant angular velocity. Weight of baseball is 5.25oz (.328lb). What is the force that is imparted on the ball tangent to the wheel and with what velocity does it exit with? I know degrees over which the ball is acted on by the tire as .581radians.

2. Relevant equations

I am unsure of which equations will be relevant. Maybe vf^2=vo^2 +2as, Torque =Force x Radius, Power = omega(angular velocity) x Torque, F= ma

3. The attempt at a solution .

The ball is acted on by the tire at arc length s. By using s=r*theta, I get s to be .059m. But the problem where I am stuck is how do I incorporate the rotation of a tire to the acceleration of the object. Once I find this acceleration, then I can easily back out the tangential force, torque and resulting velocity. Please feel free to change units if you prefer. Thanks for your help!