Angular acceleration in baseball

• rithmicspiral
In summary, the angular acceleration of a rotating system is determined by the torque, which is equal to the force times the distance from the axis. When a hitter's axis/spine slides forward while rotating, they are able to achieve higher bat speed due to being able to maintain the same torque against the ground. However, if the person is moving, they may not be able to push against the ground with the same force as a stationary person, which can affect their ability to achieve a large angle of rotation and ultimately impact their bat speed. Additionally, the tension in the arms and the shifting of weight from the back to the front leg can also play a role in increasing the distance of the ball during a swing.
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!

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!

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.

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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.

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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.

What is angular acceleration in baseball?

Angular acceleration in baseball refers to the rate of change of the angular velocity of the ball as it moves through the air. It is a measure of how quickly the ball's rotational speed is increasing or decreasing.

How is angular acceleration related to pitching in baseball?

Pitchers use their arms to generate angular acceleration on the ball, which causes it to spin and creates movement and velocity. The greater the angular acceleration, the faster the ball will spin and the more difficult it will be for batters to hit.

What factors affect angular acceleration in baseball?

The main factors that affect angular acceleration in baseball include the pitcher's arm strength, the movement and grip on the ball, and the aerodynamics of the ball in flight. Wind and air resistance can also play a role in the ball's angular acceleration.

How is angular acceleration different from linear acceleration in baseball?

Angular acceleration refers to the change in the rotation of the ball, while linear acceleration refers to the change in the ball's speed or direction in a straight line. In baseball, angular acceleration is more important in terms of creating different pitches and movement on the ball.

How is angular acceleration measured in baseball?

Angular acceleration is typically measured in radians per second squared (rad/s^2) or degrees per second squared (°/s^2). This can be calculated by measuring the change in angular velocity over a specific time interval.

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