Physics of Baseball: Understanding Angular Velocity

[Numeriprimi]

Hey, do you ever play baseball? :-) Me yes and I really like it.
However, I don´t understand physics of basseball. Today, I found one interesting about it.

Let us consider the following model of a baseball player hitting a ball. Baseball bat is a thin homogeneous rod of length L and mass m. The bat can only rotate around an axis perpendicular to the axis of the bat that is located at its end. The bat is rotating with an angular velocity ω. How far from the end of the bat should the player hit the ball in order to minimize the force with which the bat acts on the player's hands?

I don´t have any great idea about it... It is it pendulum, but what more? I know some formulas about pendulum, but I don't know, how can I use angular velocity ω...

I found a lot of interesting pages:
http://www.physics.usyd.edu.au/~cross/baseball.html
http://www.acs.psu.edu/drussell/bats/cop.html

Have you got any idea how to use angular velocity ω in formula of question?

 

[HallsofIvy]

Hey, do you ever play baseball? :-) Me yes and I really like it.
However, I don´t understand physics of basseball. Today, I found one interesting about it.

Let us consider the following model of a baseball player hitting a ball. Baseball bat is a thin homogeneous rod of length L and mass m. The bat can only rotate around an axis perpendicular to the axis of the bat that is located at its end. The bat is rotating with an angular velocity ω. How far from the end of the bat should the player hit the ball in order to minimize the force with which the bat acts on the player's hands?

It's a bit more complicated than that. The bat does NOT "only rotate around an axis perpendicular to the axis of the bat that is located at its end", it rotates around that axis but the hands that hold the end of the bat are moving so the motion of the bat is much more complicated than that. If it were just a matter of "mimimize the force with which the bat acts on the player's hand", you would want to move your hands as far apart on the bat as possible. That's essentially what you do when bunting. If (as is more commonly the situation) you want to maximize the force the bat applies to your hands, and so you are applying the maximum force to the ball, you would want to move both hands down to the end of the bat. Of course, in both "batting away" and bunting, the power applied is not everything. You would also want to maxize control of the bat and that is often done by moving the hands up on the bat.

I don´t have any great idea about it... It is it pendulum, but what more? I know some formulas about pendulum, but I don't know, how can I use angular velocity ω...

I found a lot of interesting pages:
http://www.physics.usyd.edu.au/~cross/baseball.html
http://www.acs.psu.edu/drussell/bats/cop.html

Have you got any idea how to use angular velocity ω in formula of question?

 

[Vanadium 50]

You might want to read the book "The Physics of Baseball" by Bob Adair.

 

[Numeriprimi]

Ok, thanks :-) I will read it.
However, if you have a easy model which I described, how can I do it?

 

[sophiecentaur]

You are presumably referring to the 'sweet spot', where there is no 'jarring' of the bat in your hand caused by the bat not rotating about the axis of the wrist on impact. There is a slightly easier problem which you might address first and that is "Where is the best place to put a door stop to impose least stress on the hinges when the door strikes it?" You can place the stop so there is no stress at all on the hinges.

It's basically the same question but the hinges and the door stop are both stationary and there are fewer other tricky variables involved (not least, the fact that the door can be regarded as having a uniform mass distribution over its width - unlike a baseball bat).
Can you think of a way to approach the door problem first?