Tuesday, February 2, 2010

The Moment of Inertia (Pennukanal part-2)

“Now, here’s a very interesting question.”

“Yes Ram”

“The earth rotates around its axis”

“Yes…so?”

“And it rotates from west to east.”

“What’s your question?”

“I’m coming to it. Now imagine, all people on earth start walking from west to east”

“Okay?”

“Here’s the question, listen very carefully. If this goes on for a while - that is, if these people keep walking across the earth as I said, long enough, eventually, will the earth slow down, and soon, will it start rotating in the opposite direction?”

“Why would that be? I didn’t understand.”

“ Newton’s second law of motion, every action has an equivalent and opposite reaction”

“I thought that was the third law.”

“Yeah may be, but that’s the law”

“Okay so?”

“You don’t understand. See, when you walk forward you exert a certain amount of force on the earth in the reverse direction”

“So?”

“So? This force will have the effect of slowing down the earth’s rotation”

“Hmm”

“I hope you are getting me, this force, like any other force will have to cause deceleration. Now, this effect may not be much initially, but if there are enough people waking and they walk for enough time, I am postulating that there would have to be a perceivable deceleration in the earth’s speed of rotation.”

“Interesting, that does make some sense”

“It makes a lot of sense, and what I think is, if this goes on for long enough, the earth will one day stop rotating, and then one day, it will start rotating from east to west.”

“Let me think…but… see there are oceans in the middle, people won’t be able to walk all the way”

“Okay, imagine there are no oceans, it’s all land”

“Oh okay, no oceans…but still…”

“What?”

“Well, but after a while, won’t all these people want to go back home?”

“Okay, imagine, nobody has homes, they are all homeless people who do nothing but walk from west to east”

“Let me think…”

“Yeah, sure, it will become clear to you once you think”

“No, it can’t be…”

“What? What do you mean? What cannot be?”

“I feel there is something fundamentally wrong with your whole argument, can’t quite place it though”

“Oh come on, imagine there is a log floating on water and you are walking on it, it is the same principle”

“But that’s different”

“How the hell is that different?? Or ok, think of walking on a moving train, in the direction of the train’s movement”

“Does it affect the speed of the train?”

“Of course it would, but it will have to be an endless train, otherwise the effect would cancel out when you reach the end of the train and hit its wall”

“Endless train… never thought of it”

“Yea, I’ve been thinking about this for a while now. As another example, imagine there is a ball fixed on an axis on which it’s free to rotate, imagine a few ants walking across over it”

“Will it rotate?”

“Yes, it should, if there are enough ants and they keep at it long and hard enough…theoretically… but the ants were difficult to control”

***

“Hmm….but Ram… you see when you walk, you exert a force against friction”

“Yes, so?”

“So, there is already a force acting against you, the force you exert acts against that. So they should cancel each other out, shouldn’t they?”

“I didn’t get that, please explain that to me”

“I mean Ram, the net force you exert against the earth is zero”

“Ok, but there is a net force you exert in the forward direction, else you won’t move forward, would you?”

“Yes I see your point, but you need to also consider the dynamics involved in the walking process, the backward thrust happens when you launch your foot in the walking action, and this effect is reversed when you land your other foot.”

“Okay then, assume the take off thrust is always more than the landing thrust, so that there is a net force in the forward direction all the time”

“But then that means you will have to keep accelerating…your velocity will always be on the rise”

“Yes, so?”

“No, I was just thinking, if you take into consideration the moment of inertia and angular momentum of the entire system…”

“Now why do you need to bring moment of inertia into this?”

“We’re talking about a rotating body, we have to bring in moment of inertia”

“Okay whatever, go on”

“See according to the law of conservation of momentum, the total momentum of the system should remain constant”

“So?”

“Well, so when you apply that to a rotating system, the total angular momentum should remain constant. It’s like there is no energy coming into the system, no energy going out, so the total energy has to be constant”

“But what about the energy from the sun? There is always energy coming into the system from the sun”

“Okay ignore the Sun”

“What? Ignore the Sun??”

“Come on, we don’t have oceans now, do we? Now stretch that a bit, let’s take the sun out of the system”

“Okay….”

“So, we are talking about a rotating system, parts of which are rotating with a greater angular velocity than the rest.”

“I didn’t understand.”

“Okay, imagine the earth to be made of multiple spherical shells, each capable of rotating independently of the others. If you consider this, the layer of people who are running from west to east is one such shell which can be seen to be rotating independently from the shells beneath it.”

“Okay…?”

“This exterior most layer of people is constantly accelerating as you said earlier, but it does so at the expense of all the layers beneath it. So, if you just look at the system of shells except the exterior-most one of the running people, yes, it does slow down, but you have to bear in mind that this is compensated by a corresponding increase in the angular velocity of the exterior shell. The total angular momentum of the entire system remains constant.”

“So?”

“So, the earth may slow down and even stop and then rotate in reverse direction, but the people who are running from west to east will end up running with much greater angular momentum than the earth ever had to rotate with. And if they ever stop, it will be like hitting the end of your endless train; the earth will start rotating in the usual direction again”

She looked at Ram, with an expression that bordered on mild contempt. Ram looked back, his eyes betraying the strain within his brain. Little unwelcome beads of perspiration surfaced on his brow. He felt a strange kind of fear gripping him, he looked above, as if he were about to be attacked by monstrous rotating globes from outer space. A sudden urge to run away from the living room took over him.

“Which way is the bathroom?”, he finally asked.

***

“How’d it go Ram? Did you like her?” His father asked

“I’m not sure…I need to think..”

“What? was the wavelength not alright??“

“No…no… the wavelength and all seemed good…pretty…very good…”

“God, at last!” Gasped his mother

“But…”

“Then what?”

“I need to think…” said Ram, still looking puzzled.

***
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