Angular acceleration in baseball

[rithmicspiral]

I have coached and taught baseball collegiately and professionally for the past 15 years and have stumbled upon a question that is beyond my math education.

How does linear movement of a rotating system effect the angular acceleration of that system if the system is moving left to right and rotating clockwise as it slides linearly?

Ex.
How will the stride of a hitter whose axis/spine slides forward (toward the pitcher) effect the angular acceleration of his hands as opposed to the angular acceleration experienced by a hitter's hands whose axis is fixed? I know from experience that the hitter with the fixed axis has more bat speed but would love to know the formula(s) that supports the math behind the idea. Unfortunately, when I tried to explore the answer on my own, the math was beyond my coursework. Thanks in advance for any help!

 

[rithmicspiral]

Woops. Posted a response to my own inquiry.

I have coached and taught baseball collegiately and professionally for the past 15 years and have stumbled upon a question that is beyond my math education.

How does linear movement of a rotating system effect the angular acceleration of that system if the system is moving left to right and rotating clockwise as it slides linearly?

Ex.
How will the stride of a hitter whose axis/spine slides forward (toward the pitcher) effect the angular acceleration of his hands as opposed to the angular acceleration experienced by a hitter's hands whose axis is fixed? I know from experience that the hitter with the fixed axis has more bat speed but would love to know the formula(s) that supports the math behind the idea. Unfortunately, when I tried to explore the answer on my own, the math was beyond my coursework. Thanks in advance for any help!

 

[Lojzek]

The angular acceleration is always determined by the torque:

alfa=M/I, M=torque=F*r, I=moment of inertia

So if the hitter would be able to move forward and still maintain the same torque (against the ground), he would achive higher bat speed.

If it does not work in practice, the cause is probably that a moving person can't push his legs against the ground with the same force as a standing person. Or maybe he can't get enough the distance between his feet and at the same time direct the force perpendicular to that distance: F*r should be maximized (more accurately F x r, so only perpendicular component of F counts). The other important parameter is the angle of acceleration: if you rotate your body by a greater angle (at the same angular acceleration), then you will achive a larger angular velocity. Again it is probably easier to achieve a large angle of rotation if you do not move forward.

 

[rcgldr]

Don't forget the pendulum effect. The bat is held at one end, while it's center of mass accelerates outwards during a swing, similar to a golf swing. If I understand this correctly, most of the torque is due to tension in the arms, and not torque force applied at the wrists. The tension in the arms is a function of the torque and centripetal force applied through the shoulders via the upper body though. In the case of golfers, some forwards shifting of the weight from the back leg to the forwards leg, mostly at the hips, will increase the distance of the ball on a drive.

 

[Lojzek]

In the previous post I was thinking about maximizing the angular momentum of the whole body and I forgot about the importance of focusing the angular momentum from the whole body to the bat. However this part is less dependent of the speed of the axis, so it probably does not affect the conclusion.