# Reaching Max height with a baton using physics.

## Main Question or Discussion Point

I am working on a project and the topic is: Figuring out what the maximum height of a baton tossed vertically can be. I have never taken a physics class, so this is all completely new to me. I have been working for a little while now, and I didn't know if there were any ideas or equations anyone had for me.

Here is the basics of the problem again:
Baton Length: 30 inches
Being tossed straight up
It is rotating vertically to the floor (similar to the rotation on a windmill I suppose)
I have a few different trials and numbers for those trials including rotation time, number of rotations, peak rotation...
I have noticed that the baton takes longer to rotate on the downfall.

Any info would be great!

Related Other Physics Topics News on Phys.org
why would you even want the baton to rotate?
are you limited to launching it by hand?
find a way to launch it straight up like a very long bullet! With sling shot, bow, cross bow or something...

what are the rules here?

Throw it hard enough and it will reach infinity, what are you using to launch it?

256bits
Gold Member
I have noticed that the baton takes longer to rotate on the downfall.
Yeah. I wonder what causes that, but it does appear to be the case when you throw a stick into the air and the stick is rotating. I would guess that it is some type of optical illusion. From the ground looking up it is difficult to tell when the highest point is reached especially when the object is rotaring.

Of course it is rotating less on the way down, it was actually rotating less on the way up too...because of air, there is drag and so the baton tends to rotate less and less from the very first instant you let go...it is just that on the way up it has a lot of energy and spins a lot, too much for your eyes to keep up, unlike the way down...

The thing is that when you throw baton by holding one end, it is almost like using one end of the baton to throw the other one...it is a bit better than that, it is just that a piece of length in the baton benefits less and less from the throw's acceleration, the close it is to your hand...and so, it leaves rotating.

...that's why I initially suggested to use a device to accelerate the entire baton to the same value and shoot it straight up, no rotation...and, of course, you wouldn't be limited by the human body's arm.

256bits
Gold Member
Gsal. Your posts is understandable, and is the way to do it.

For a rotating baton though, and neglecting air resistance:
I think the eyes focus on the edge of the baton rotaing up when the whole baton is moving up, and that end looks like it is rotating faster since the translational and rotational velocities of that end add together.
On the downwards trip of the baton, the eyes are focusing on the end rotating up and moving down so the translational and rotational velocities subtract from one another and the baton looks like it is rotating slower.
At least that is what I observed and concluded from my non-scientific study, conducted over many attempts of throwing sticks in the air as a kid.

256bits:

I appreciate your worldly experience in stick throwing and admit that I don't recall paying much attention when doing so myself...

...but given the physics of the baton throwing procedure using one end of the baton to launch the other, I proposed for your consideration that the center of rotation IS NOT half way down the length of the baton; instead, it is closer to one end than the other...and so, one end of the baton is effectively moving much faster than the other at all times...

...of course, if you were a real cheerleader with a baton and are able to do that thing where they spin the baton from the middle and THEN throw it up...that's another matter and I am sure it does not go as high...

Anyway, any thoughts about the 2nd paragraph above?

gsal

256bits
Gold Member
It doesn't matter how the object is made to spin, either by holding it in the middle or from one end. Once ejected from the hand and flying throught the air the object will rotate about its centre of mass or centre of gravity. The rotaional velocity of any point on the baton is directly related to its distance from the centre of mass. Add in the translational velocity and you can find out the actual velocity of any point on the baton.

Suppose you throw the baton so it lands some distance away instead of straight up. The centre of gravity will follow the famous parabolic curve of an object being acted upon in a gravitational field so close to the earth in a short distance, whether of not the baton is rotating or not. All other points on the baton follow different trajectories depending on the rotational velocity. The cg is the only point that follows the parabola.

If we assume a symmetrical baton then:
If as you propose one end of the baton always rotates faster than the other end then that end would have a rotational force associated with it that is stronger than at the other. Call that force the centifugal force. The faster rotating end would want to fling out and pull the other end along. The baton would end up going to wherever the fastest end is pointing to as you release it which does not happen.

Both ends take turns going faster or slower in the direction of travel if the baton is rotating as it moves along.

In response to many of the questions, I am "launching" it by hand. I am a baton twirler and interested in figuring out maximum height for my own tosses. So, no "launching machines" will be used. I have been working with the various programs including video of my tosses to analyze the number of rotations and the time it takes for each rotation. My trials have shown that the rotations directly after the release are faster than the ones on the downfall of the toss. I feel this might have something to do with the force caused by the preparation and the actual toss.

The video footage I am working with captures the toss straight on from a frontal view. I am able to see not only the entirety of the toss, but the pattern of the arc the travel makes as well. When the toss is done, there is a rotation, similar to a windmill, that occurs. I am releasing the baton from the CENTER of the baton. That is one of the foundational skills that is taught in the very early years of being a BATON TWIRLER (not a cheerleader, completely different things... lol). The problem is not dealing with no rotation, that would be simple enough, it is dealing with the fact that it does have that windmill like rotation to it.

Before the toss there is a "wind up" that occurs where the baton is in a spinning state, so to speak, before the toss is initiated. This gives more drive and force into the toss, resulting it to spin faster and generally go higher.

The path that the baton travels in after the release does result a parabola facing downward. In my trials, the baton generally only shifts over to the left as opposed to forward or backwards.

Thank you all for your ideas thus far. It is really helping me to think about different aspects of this and having to explain it to others. :)

256bits
Gold Member
Thank you all for your ideas thus far. It is really helping me to think about different aspects of this and having to explain it to others. :)
Where is the video???

If you can make sense out of our mumbo-jumbo and interest then all the best.

256bits:

I stand corrected...no matter how I throw the baton, once released it should spin about its center of mass.

BatonAgnel:

I am not sure how "wind up" of the baton gives it more energy; to be sure, it makes it easier to know where the center of mass is ('cause it spins about it) so that you can focus all your might into it...as oppose to any other point along the body of the baton...it is a matter of efficiency, I guess.

If anybody knows the physics of the "wind up" and whether it truly benefits, I would like to hear about it...benefits other than stability...benefits towards height.