Solving the Twist: Athlete's Angular Momentum and Stopping Movements

[Winner]

Hey ,

The question:

The athlete on the diagram (linked) is free in the air and has a total angular momentum as indiated by the red vector.

1)Indicate with a vector the direction of his twist based on his orientation and angular momentum, show how you got this.

2)Describe 2 different movements he could make to stop his twisting while in the air, explain.

Link here:

http://www.geocities.com/saint_biron/gymrotate.JPG"

1)By dividing the angular momentum into it's parts, I can get the rotation about each axis, as I've done.
So with the horizontal axis, and USING the right hand rule (ie thumb points in directin of angular momentum, and fingers wrap around axis, or rotate in that direction. The horizontal axis will be rotation backwards and the vertical axis is rotating clockwise?

2)I think you can stop the movement by raising the right hand or dropping the left hand. But are these different? They work because that way, the body position is symmetrical and the angular momentum in each axis is 0?
Thanks

 

[mezarashi]

For (1), the right hand rule can always be used to find the direction of rotation given the angular momentum vector. If you are required to find the twist along an axis, then decompose the angular momentum vector onto the various axes as well. Apply the same rule to each axis.

For (2), what does the conservation of momentum say. Momentum of a closed system is always conserved in the absense of external forces. Can the athlete do anything by himself to absolutely 'stop' his movement?

 

[Winner]

So, in my diagram I outlined the directions, did I do these right?

I don't think he can "stop" his movement of falling down, but he can stop twisting. As I've noted, he might be able to life his right hand OR drop his left but are those considered different? By doing that he balances out his body.

 

[mezarashi]

So, in my diagram I outlined the directions, did I do these right?

In general I think they were alright. If your sure your using your rules correctly, I don't see a problem. The approach is valid.

I don't think he can "stop" his movement of falling down, but he can stop twisting. As I've noted, he might be able to life his right hand OR drop his left but are those considered different? By doing that he balances out his body.

This is what I'm afraid you may be misunderstanding. If you're in the air spinning, what can you do to stop you from spinning. Let's suppose you are in space for the simplicity of the argument. You try to grab on to your arm and pull back to stop, but by Newton's third law, every force has an equal and opposite reaction. You're going no where.

Unless external forces are involved, momentum is conserved: angular and linear.

You CAN however change the speed of your rotation. Take for example the ice skater. When she pulls in her arms, she can make herself spin much faster, then slow down when she pushes out her arms. Because angular momentum is conserved, by changing her moment of inertia, she can change angular velocity.

 

[Winner]

So are you saying that if my guy spreads himself out, he'll eventually stop twisting because of his large Inertia which gives a small angular velocity as in H(ang momentum)=Iw? So can I say he can spread his hands out and spread his legs out as two different movements OR are they the same, ie. based on the same concept.

My teacher mentioned something about how a cat can twist so that when dropped from it's back it can land on it's legs. Something like by twisting his waist in opposite direction of upper body and then twisting the waist back in the same direction so all legs face down. Don't know if that has anything to do with it.

 

[lightgrav]

An athlete is NOT a rigid body.
Whereas the TOTAL angular momentum is fixed (ignoring air resistance),
he can keep his feet underneath his shoulders (stop his BODY rotation)
if he transfers all that rightward (to HIS right) L into his arms
(top arm goes back into page, lower arm goes forward out of page)
and keeps it there (arms continue to rotate around shoulder joints)

 

[mezarashi]

So are you saying that if my guy spreads himself out, he'll eventually stop twisting because of his large Inertia which gives a small angular velocity as in H(ang momentum)=Iw? So can I say he can spread his hands out and spread his legs out as two different movements OR are they the same, ie. based on the same concept.

No, I said he can slow down to conserve angular momentum. I'm not very clear with your question now at this point. He can stop rotation of some parts of his body if he is willing to let other parts rotate in its place. The point I'm making is that, while he is in the air, his total angular momentum is constant. He can play around by transferring this momentum to various parts of his body, say arms, or legs, but once he is off the ground, his angular momentum is fixed. This applies to ice skating, diving, pole jumping, etc. In reality there may be slight changes due to air resistance, but I'm only discussing in principle.

My teacher mentioned something about how a cat can twist so that when dropped from it's back it can land on it's legs. Something like by twisting his waist in opposite direction of upper body and then twisting the waist back in the same direction so all legs face down. Don't know if that has anything to do with it.

You can twist and turn around because our bodies are not rigid. For some parts to turn one side, other parts may need to go the other. The beginning and final angular momentum should nonetheless be the same, but I'm afraid of repeating myself again.

 

[Winner]

See, now I'm really confused...Ok, it says describe two ways which we can stop his twisting while still in the air.

So what Lightgrav suggested was 1)lift his right hand out of page and drop left one--wouldn't this cause him to start twisting the other way?
2)aren't his feet always beneath his shoulders?How does that stop body rotation?

Mezarashi:

You had the skating example. So if you tighten up your body, you can spin faster. So why is it that I can't spread out in mid air to slow down my twisting to small amount such that twisting stops. Your angular momentum is still conserved, but like you said, I increased my I by decreasing my ang. velocity. That makes sense to me, no?

Ahhh, . This seems so difficult, but the solution is probably really simple

 

[Winner]

Wait, got an idea...What about if he rotates his leg in the opposite direction of his hand rotation?


Ok..I'm going to go bang my head on the table now lol. This is nuts.

 

[mezarashi]

See, now I'm really confused...Ok, it says describe two ways which we can stop his twisting while still in the air.
So what Lightgrav suggested was 1)lift his right hand out of page and drop left one--wouldn't this cause him to start twisting the other way?
2)aren't his feet always beneath his shoulders?How does that stop body rotation?

Like I said, he can rid some parts of his body of rotation if he transfers the rotating to other parts to conserve momentum. Also, he can't keep twisting a certain direction forever can he? At some point he will need to twist the other way or stop twisting.

So why is it that I can't spread out in mid air to slow down my twisting to small amount such that twisting stops. Your angular momentum is still conserved, but like you said, I increased my I by decreasing my ang. velocity. That makes sense to me, no?
Ahhh, . This seems so difficult, but the solution is probably really simple

Angular momentum can be written as:

$$L = I\omega = mr^2 \omega$$

in the case of a point mass. Now, to have omega approach zero, r would need to approach infinity. He is not able to stretch his arms infinitely out. His rotation will never be zero. If you consider physical principles in your logical steps, you will find that many of your own arguments can be answered.

 

[NotaPhysicsMan]

I think after watching some gymnast do twists in air and landing, I've figured something out.

It definitely has to do with hips and arms. He can stop his twist near the end before landing, because he has turned most of his angular momentum around the transverse axis, where somersaulting takes place. On a video I saw, there's no twist before landing, so he must have stopped it.