What role does a person's reach play in generating velocity (i.e. when swinging a bat)?

A baseball players bat swing is parallel to centripetal acceleration. It's defined as:

cent._accel = v^2/r

Rearranging, you get r = v^2/[cent. accel]. Keeping centripetal acceleration constant, you can see that the radius and velocity are directly proportional (i.e. if r increases, v increases, and vice-versa).

That is why that a person's reach affects generating velocity. If his arms are longer, that resuls in a longer radius, causing velocity to increase from the above relationship.

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Hope this helps

Well linear velocity (v) is related to angular velocity (ω) by the relationship

v = rω where r = radius of curvature

So the larger the radius (ie the longer the reach) the faster the velocity for any particular angular velocity.

the longer the arms (aka reach) the higher the bat speed. loosely