A scientific question of momentum

[Queenie]

So, I have a question.

Assume I am standing, and want to get to the ground as quickly as possible, squatting, etc no matter, assume I am dodging some sort of blow to the head.


My question is, which way will be quickest? I know that from gymnastics that we throw our arms up to aid in momentum- you can demonstrate this by throwing your arms up on a trampoline and acquiring some bounce.

But I wonder, which way will be quicker, as if we throw our arms up it should have an equal and opposite force but likely more complicated if the air is just involved.

So I ask, what would be quicker, if standing and wanting to fall faster-

throwing our arms up in an attempt to make us fall faster, or throwing them down in an attempt to increase our momentum?

I would like some discussion of physics and why, so I can increase my understanding of the matter.

[SLATYE]

The best you can achieve is having your centre of mass accelerate downwards at 9.8m/s/s (ie gravity). No amount of flailing around is going to improve that; as long as your feet are off the floor (so there's nothing holding you up) you'll achieve it.

What throwing your arms up will assist with is moving your centre of mass relative to bits of you that need to be protected. This is important if you want to get your torso and head out of the way quickly, but you don't really care what happens to your arms. Suppose you mass 100kg total, and your arms make up 10kg of that. They start at head height, and in throwing them up you move them to 0.5m above head height. Your legs mass 20kg and are initially 1.5m below head height. When you squat they move to 0.5m below head height. The rest of your body weighs 70kg and is always 0.5m below your head.

Now, Chuck Norris tries to kick you in the head so you immediately try to get your head down by a distance of 20cm. Getting the weight off your feet means that your CoM is accelerating downwards at 9.8m/s/s, but I'll call it 10m/s/s for simplicity. It'll take 0.2 seconds for your head to drop to a suitable level, and in that time you get kicked in the head sixteen times.

As an alternative, suppose that you immediately raise your arms and legs. This immediately causes your centre of mass to move from [(70 * -0.5 + 10 * 0 + 20 * -1.5) = -65cm] 65cm below head height to [(70 * -0.5 + 10 * 0.5 + 20 * -0.5) = -40cm] 40cm below head height. This all happens instantaneously because you've got insane reflexes. Since no external forces are acting on you in this time (they can't, since force requires time) your centre of mass doesn't actually move relative to the world; it only moved relative to your head. The only possible outcome is that your head moves down to compensate, in this case by a distance of 25cm. No more being kicked in the head! Of course, immediately after this gravity does apply, and then your centre of mass accelerates downwards relative to the world at 10m/s/s. However, the important thing is that you essentially got the first 25cm out of the way instantly, without having to wait for gravity.

It's also worth noting that legs matter much more than arms here, because they're both longer and heavier.



Throwing your arms down is an interesting idea. I can only assume that it'd be done to take advantage of different response times between the arms and legs. In an ideal world (ie instant responses), throwing your arms down would just push your head up (relative to the world) and get you decapitated by the kick. However, if your legs are slow to respond, then throwing your arms down before your legs do anything will essentially shift your centre of mass downward relative to the world; your head doesn't move upwards because any force generated by pushing your arms down just goes towards reducing the load on your feet. This means that when you later throw your arms up, you get a bit more movement of the head and torso than you'd have gotten otherwise.

[aXis]

Slayte pretty much nailed it.

The best you can achieve is for your centre of mass to accelerate downwards at 9.8m/s^2. Getting your head out of the way faster will be achieved by changing your body distribution - raise your arms AND legs, and as a result your head will be drawn down to compensate.

[luxtin]

Is there any chance you could duck, use of muscles in a diving fashion, at a speed greater than that of the force of gravity?

[Benno1988]

Originally Posted by luxtin

Is there any chance you could duck, use of muscles in a diving fashion, at a speed greater than that of the force of gravity?

I don't think so. I think any form of thrusting relative to your own weight just shifts your own body. If you had something solid above you to push off then you could accelerate faster than gravity.

[luxtin]

Originally Posted by Benno1988

I don't think so. I think any form of thrusting relative to your own weight just shifts your own body. If you had something solid above you to push off then you could accelerate faster than gravity.

Muscles can move your body independent of gravity. Also don't you start off falling slowly and build up to 9.8m/s.

Think about the difference between diving into water compared to a belly flop.

[Benno1988]

Originally Posted by luxtin

Muscles can move your body independent of gravity. Also don't you start off falling slowly and build up to 9.8m/s.

Nope. From the moment you are in freefall, you'll have an acceleration toward earth of 9.8m/s/s. So, ignoring any other factors like air resistance, you'll be at 9.8 m/s after 1 second.

Muscles do move your body independent of gravity. Hence why I don't think thrusting your arms up or down helps with how fast your body moves toward the ground, purely helps the shape of your body. So it could get your head toward the ground faster but at the expense of some other body part.

Originally Posted by luxtin

Think about the difference between diving into water compared to a belly flop.

I don't get what you're trying to explain? The difference in that example is due to the difference in resistance each 'shape' offers in water, or air for that matter.

[luxtin]

Yea its a no brainer that in free fall flailing your arms about wont do anything. Changing your aerodynamics will though but the question presumes that we are standing, not in free fall.

My physics is rusty high school stuff but from recall you accelerate up to a certain point. The first 3 or 4 metres isn't that fast.

[Bastard Child]

Originally Posted by Benno1988

From the moment you are in freefall, you'll have an acceleration toward earth of 9.8m/s/s.

So what would be the gravitational acceleration be when you're standing up?

[Benno1988]

Originally Posted by Bastard Child

So what would be the gravitational acceleration be when you're standing up?

The same of course

@ Luxtin. In free fall you'll accelerate up to the point of terminal velocity, which is dependant on a few different things, yes.

[luxtin]

Get a battery, like a AA, in your left hand drop it from head height and see if you can get your right hand to the floor before it.

[Benno1988]

Originally Posted by luxtin

Get a battery, like a AA, in your left hand drop it from head height and see if you can get your right hand to the floor before it.

Battery isn't connected to my arm which is connected to my shoulder which is connected to my torso which is connected to my waist which is connected to my legs which are resting on the ground.

[luxtin]

Yea but it shows that the acceleration of 9.8m/s is not overly fast in the first two metres which is what we are contending with.

Another example. Michael Jordan can defy gravity using his muscles and jump almost 1 metre from a standing position. So surely someone like a professional wrestler can use his muscles and go with gravity to increase the comparable speed.

[gdjacobs]

As a wrinkle, reducing your rotational moment of inertia by drawing in your arms would allow you to more quickly twist and present less of a profile to your attacker.

[Benno1988]

Originally Posted by luxtin

Yea but it shows that the acceleration of 9.8m/s is not overly fast in the first two metres which is what we are contending with.

Another example. Michael Jordan can defy gravity using his muscles and jump almost 1 metre from a standing position. So surely someone like a professional wrestler can use his muscles and go with gravity to increase the comparable speed.

An elite athlete would be able to manipulate their body shape within space much better than we can. The fact that they would still accelerate toward earth at 9.8m/s/s would remain. I dont see how one could accelerate faster toward earth without the use of something to 'push' off.

Wonder if being trolled