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

Question

okay, I know longer reach=higher velocity, but I want to know WHY.

Answer 1

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

Answer 2

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.

Answer 3

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