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/sci/ - Science & Math

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11322206 No.11322206 [Reply] [Original]

Here's one for the ones who grapple with mechanics. A boy is seated on a carousel. The carousel is turning at a constant speed that isn't zero. There's no friction; the acceleration is 0. Suppose the boy is lifted off of the carousel in a perfect motion that doesn't disturb the carousel. What happens:
Does the carousel turn faster when the boy is lifted off? Or faster? Or does it keep turning at the same speed?

>> No.11322228

>>11322206
I think you must mean there's no angular acceleration, because by definition, something that is constantly changing its velocity vector (as in the case of sitting on the edge a rotating object) is accelerating.

>> No.11322237

OP just wants to steal children from carousels, do not help him.

>> No.11322249

>>11322206
The speed does not change

>> No.11322270

>>11322206
>Suppose the boy is lifted off of the carousel in a perfect motion that doesn't disturb the carousel.
>that doesn't disturb the carousel
By definition, no change in speed, though the rotational momentum is of course lowered.

Do I win your homework?

>> No.11322279

>>11322249
>>11322270
I was going mad because everyone around me including my professor claim that it increases in speed. I'm adamant it stays the same. Thanks for being radical with me.

>> No.11322286

>>11322279
Your professor is dumb as fuck.

Let's say the boy is just standing on the carousel. His only interaction with the carousel is the friction through his shoes. The forces from him standing on carousel interact solely with the pivot, and not the spinning mass. Him leaving the platform does not interact with the remaining spinning mass.

>> No.11322290

>>11322249
What's the conserved quantity here? Energy or angular momentum?
This should show you that the "speed" does change.

>> No.11322294

>>11322290
Do you have a spinning office chair? Spin on it and get up mid spin, does the chair speed up? Furthermore, does it spin faster the heavier you are?

Anyone saying the speed changes is a dumbass.

>> No.11322298

>>11322206
dumbasses its fastre, havent u ever looked at an engine

>> No.11322307

>>11322206
I think it would stay the same speed.

If it would accelerate, that means a force acted on it that pushed it in that direction.
But here we assume that it just loses connection to an extra weight. That doesn't push it forward, right?

HOWEVER, the carousel now has less weight, so the motor that drives the carousel has an easier time to reach a high speed, that's probably why people think it makes it go faster.

>> No.11322331

>>11322307
>HOWEVER, the carousel now has less weight, so the motor that drives the carousel has an easier time to reach a high speed, that's probably why people think it makes it go faster.

Exactly, I'm pretty sure that everyone who think it increases the speed get that intuition from an ill conceived use of that fact. You'll be able to accelerate it to a higher speed with x energy if it's lighter, but the boy doesnt give off his kinetic energy to the carousel when he's lifted off so him being lifted off doesnt fucken increase the speed of the carousel.

>> No.11322350
File: 21 KB, 584x734, fatass.png [View same] [iqdb] [saucenao] [google]
11322350

>>11322331
correction: it won't be possible to get it to a highter speed using x energi just by the system weighing less. If it's lighter but the weight is extended, like, 20 miles from the center, it'll still reach a lower speed than a fatass sitting two foot from the center. point still stands, tho.

i dont know if my drawing helps anyone

>> No.11322364

>>11322206

If the boy jumped such that his speed was 0 relative to the ground, the carousel's speed *would* increase, note that to do this he must exert force on the carousel.

If the boy jumped directly into the air (applying a perfectly downward force) he would continue to move at whatever instant velocity he started with and the carousel's speed would be unchanged.

It is easy to conflate the cases in the given scenario, but as you describe it, it is the second case with the addition that the boy transfers some momentum to whatever lifts him, which accounts for the discrepancy.

>> No.11322368

I want to know what kind of professor would get something like this so terribly wrong. What kind of shithole ""university"" do you frequent, OP?

>>11322206

>> No.11322370
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11322370

The total angular momentum of a system does not change without external torque. Take the origin to be the center of the carousel. The initial angular momentum is [math] L=(I+mr^2)\omega [/math] where I is the moment of inertia of the carousel itself (without the boy), m is the mass of the boy, r is the radius the boy sits from the origin. Everything is in UCM at the moment. Now the boy is lifted off. There are two very important details to consider: what is the motion of the boy after being lifted off the carousel, and what exactly is our system?
If the boy is lifted vertically off the thing such that he hovers motionless over the intertia frame in which the carousel, we have it that [math] L'=L \implies I\omega'=I\omega+r^2m\omega [/math]. But since all quantities are positive, this can only be true if [math] \omega'>\omega [/math]. So the carousel speeds up.
However in real life, to lift boy up in such a way that he is motionless above the ground, there must be some device to transfer this L to, something like a crane fixed to the earth. Or if a giant lifts him up, the sudden change in L of the boy would be transferred through the tractive force in the giant's shoes to the earth (changing the rotation of the earth some minute amount). In reality, the system cannot just be the boy sitting on a carousel on an infinite inertial plane. This is what really happens, and the carousel's rotation in the frame of the real ground (which is NOT) an inertial frame ends up with no apparent change.
The professor isn't "dumb as fuck," you sophomoric retards. He's actually right, given the assumptions a class covering introductory rigid body dynamics would typically make. Blow me.

>> No.11322372

>>11322368
it's debatable whether it's a university. It's DTU, the technical university of denmark. It's somewhat renowned but...aw man. how qualified the professors are, that varies a lot.

>> No.11322376

>>11322370
>If the boy is lifted vertically off the thing such that he hovers motionless over the intertia frame
he doesn't. If he did, he'd have transferred his kinetic energy to the carousel. he doesn't. you blow me.

>> No.11322386

>>11322370
>The professor isn't "dumb as fuck," you sophomoric retards. He's actually right, given the assumptions a class covering introductory rigid body dynamics would typically make.

yet

>Suppose the boy is lifted off of the carousel in a perfect motion that doesn't disturb the carousel.

You are one dumb furry. Also lifting the boy off simply disconnects him from the rest of the spinning mass, it doesn't matter how his momentum is preserved when he is lifted off.

Easier to consider: what happens if the friction on the boy's shoes suddenly becomes zero?

There's no way to spin this: OP's professor is dumb af.

>> No.11322397

>>11322294
Answer the question. If you can't, you're automatically wrong. You talking about the "speed" of a carousel already tells a lot.

>> No.11322420

>>11322397
Answered it many times this thread. Disconnecting a mass instantaneously literally means it cannot exert the torque needed to speed up the carousel. Else you are asserting that the speed of the carousel will increase discontinuously which would mean infinite acceleration and therefore infinite power and energy. Else you are asserting that the speed will change without conservation.

There is no way to win this, friend.

>> No.11322428

>>11322206
This >>11322228
Also, "that doesn't disturb the carousel" so by the statement of your problem, nothing changes about the carousel

>> No.11322430

>>11322376
>he doesn't. If he did, he'd have transferred his kinetic energy to the carousel. he doesn't.
So then either there is an external torque on the system or the conservation of momentum is violated. Which is it?
>>11322386
>>11322420
This anon >>11322364 explains the same thing I tried to convey, maybe a little better. It's one thing to be wrong, it's another to be confidently wrong.

>> No.11322437

>>11322430
ya think the conversation of momentum is violated because he doesn't transfer his kinetic energy to the carousel? Imagine someone lifts him. When that guy does that, he'll either start to spin around himself because of the momentum of the boy. If he lifts him close to himself, he'll spin faster than if he lifts him far away. He can stop the boy if there's friction between him and the ground. Where's the violation?

>> No.11322439

>>11322420
>Disconnecting a mass instantaneously literally means it cannot exert the torque needed to speed up the carousel
A spinning figure skater bringing in his arms also does not put a torque on him, and yet he will speed up.

>> No.11322441

>>11322430
being lifted is far different from jumping. The forces required to lift the boy are sourced externally. His momentum, once disconnected, which is instantaneous in a ridgid body system, is irrelevant to the problem since it will never affect the carousel.

>> No.11322443

>>11322437
>Where's the violation?
The violation is specifically that the infinite, fixed, flat, always inertial plane that the carousel sits on, and is a common feature in undergrad mechanics, is inherently non-physical. It cannot exist. A boy simply jumping vertically up off this plane violates linear momentum.

>> No.11322446

>>11322439
>does not put a torque on him
incorrect

>> No.11322447

>>11322441
>The forces required to lift the boy are sourced externally
The problem is we disagree what exactly the system is.

>> No.11322449

>>11322446
How? His momentum is the same. There is no torque, only a change in inertia. Why are you roleplaying?

>> No.11322450

>>11322430
>>11322430
He could also be lifted by suspenders like I drew in >>11322350 . If the suspenders were attached somewhere directly above the center of the carousel, he's continue spinning just like he did before. The system (the boy and the carousel) would move exactly like before he was lifted. He spins in the air. The carousel spins on its own. No change of angular momentum.
If the suspenders are attached just above him, he'll start to swing back and forth.
If the suspenders are on a track, he'll go on and on into infinity. His momentum is preserved and so is the momentum of the carousel.
The carousel doesnt give a fuck. What kind of disturbance do u need to have to think it oges faster? Y'all think that if you take chunks out of the carousel, the remaining carousel will just keep spinning faster and faster? I really liked the thinking of the guy who imagined a fucking office chair.

The carousel turns faster if the boy moves towards the middle. It's the same thing as a pirouette. But he doesn't fucking do that.

>> No.11322456

>>11322449
Split his limbs into different weights, and the momentum of his legs and torso will increase as he moves his arms in (arm momentum will decrease).

>> No.11322458

>>11322420
Hint: angular momentum works quite like momentum. There's mass involved and if that changes, momentum changes as well. Automatically.

>> No.11322459
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11322459

>> No.11322467

>>11322458
Your assumptions about angular momentum only apply if no parts of the mass are disconnected.

>> No.11322468 [DELETED] 

>>11322456
You've never taken a physics class in your life

>> No.11322473

>>11322456
And yet there is no torque and the total angular momentum is constant. Amazing.

>> No.11322479

>>11322473
Total angular momentum is constant, correct. If your problem involves moving the arms independently, then you need to consider that they will exert torque on the rest of the spinning mass to find an equilibrium speed.

>> No.11322484

Well there's 0 friction so of course it stays the same speed. The boy doesn't disturb the carousel in any way so the carousel keeps its speed and the boy gets to keep his energy juice.

>> No.11322488

If the boy is lifted off where he is seated, the carousel remains the same.

If the boy goes to the middle and is lifted off, the carousel will go faster. It will increase in angular momentum as he moves towards the middle, though; not as he's lifted off.

If the boy moves further towards the edge and is lifted off, the carousel will go slower. It will decrease in angular momentum as he moves further from the middle, though; not as he's lifted off.

>> No.11322489

>>11322479
>will exert torque on the rest of the spinning mass to find an equilibrium speed.
And yet the rotational speed of the skater changes despite there being positively no *external* torque

>> No.11322497

>>11322489
Nice moving of the goal posts buddy. No one said anything about external torque.

>> No.11322502

>>11322206
Sit in an office chair and spin in it up to some reasonable speed, then try sticking your hands out and moving them in. Your angular speed will change despite the fact that your mass is staying the same because you're changing your mass moment of inertia. In the given problem the same principle is in play (though now the mass is changing). Removing mass from anywhere would increase the the angular speed because it would decrease the mass moment of inertia. This is the principle of conservation of angular momentum. The only exception is if the mass that you removed was a point or line of mass on the axis of rotation, since then the distance from the axis would be zero.

>> No.11322505

>>11322497
>No one said anything about external torque
I did right here >>11322439

>> No.11322513

>>11322505
You didn't say external torque. The arms are exerting torque on the rest of the spinning mass, i.e. 'him'.

>>11322502
Your assumptions of angular momentum only work provided no parts of it are disconnected.

>> No.11322514

>>11322502
when you take your arms close to your chest, you don't remove mass. You move mass closer to the center. see >>11322488 or >>11322450 .
Imagine if your arm is suddenly dislodged. comes flying off. You got the plague or something, you're half rotten, what ever floats your bots. Does that make you spin faster just like bringing your arm closer? huh?

>> No.11322526

>>11322513
>>11322514
This is a fair point that I didn't consider. I believe that the result is actually based off of the way that the removed mass moves after it is removed. Does it retain its angular momentum after removal? The original question is unclear in what happens afterwards so we can't know how the angular momentum was distributed between the two bodies.

>> No.11322532

>>11322526
I dont think there's anything that lacks in the definition. The boy goes on moving in what ever direction he had when he was lifted off, which, upon liftoff, is directly perpendicular to the direction to the center. He doesn't hang motionless. I think it's easier to imagine if you think of him as hanging in suspenders that are pulled to lift him, or if you imagine a gentle, suave hand of god. Interesting things start happening to the suspenders or the hand of god, upon lifting the boy. I tried to explain it in >>11322450 (You) . Thanks for being level headed.

>> No.11322538

>>11322513
>You didn't say external torque
Sorry for assuming you had a freshman level reading comprehension.

>> No.11322542

>>11322538
Yikes.

>> No.11322552

>>11322532
I don't think it's clear from the problem statement that the boy maintains his original velocity. We could just as easily imagine that the force lifting him up also absorbs his momentum while doing so, which might have different results. Without working the problem though it's hard to say, and either way the momentum goes with the mass when it's disconnected. Intuitively, right after the disconnect I believe that the ratio of the carousel MoI to the mass MoI should equal the ratio of the mass angular momentum to the carousel angular momentum. Since the angular moment and MoI distributions are unknown, you can't determine what happens.

>> No.11322563

>>11322552
It doesn't matter what happens afterwards. What ever he's in touch with after lift off can stop him or send him rotating around another axis or let him slid off into infinity. He doesn't transfer his kinetic energy to the carousel.

>> No.11322575

>>11322563
He doesn't transfer his kinetic energy back into the carousel, but he took some with him when he was disconnected, presumably (or maybe he didn't, that's why the question is ambiguous). Since the only energy the carousel has is rotational, some of it could be transferred to the boy when he's disconnected, and I don't think there's a way to determine how much is transferred.

>> No.11322583

>>11322563
>>11322575
>invoking kinetic energy at all
You're both retarded

>> No.11322592

>>11322583
It's quite relevant here, actually. The final angular velocity depends on two things: how much energy the boy took with him (which is going to be kinetic energy), and how much he changed the mass moment of inertia of the carousel while leaving. The more energy he takes with him the slower the carousel will ultimately move, while the more he decreases the MoI while leaving the faster the carousel will ultimately move.

Unless you're implying that energy can be created from nothing just because the carousel is spinning...

>> No.11322595

>>11322592
>how much energy the boy took with him (which is going to be kinetic energy)
Jesus christ, read a fucking book

>> No.11322600

>>11322595
Could you explain what the point you're trying to make is?

>> No.11322603

>>11322467
Sure, but if there weren't any connection to begin with, the question is moot, since the extra mass wouldn't have any effect.

>> No.11322616

>>11322279
Well the speed does change if the boy has a mass unequal to zero and isn't centered on the axis of the carousel's rotation. The unequal mass-distribution causes the inertia of the whole system increase.
I'm not that much into physics, please excuse my incomplete comment.

https://en.wikipedia.org/wiki/Parallel_axis_theorem

>> No.11322623

>>11322616

Dumb

>> No.11322628

>>11322600
The boy doesnt "take energy with him". Energy conservation is not how you approach this problem.

>> No.11322637

>>11322628
Why not? Since the problem states that there are no non-conservative forces, or at least that there's no friction and I doubt there's any other non-conservative forces that should be considered, both conservation of momentum and conservation of energy must apply here. It can be approached from both ways. One might be easier but both should give the same answer ultimately.

>> No.11322638

>>11322637
>Since the problem states that there are no non-conservative forces
An external force lifting the boy up is absolutely non-conservative.

>> No.11322643

>>11322638
That's fair. I interpreted it as doing no work on the boy and therefore transferring no energy.

>> No.11322649

>>11322206
He continues outwards due to lack of centripental force. Then it continues spining in the same speed because the angular momentum isn't changed

>> No.11322777

>>11322643
That's what I got from OP, too.