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/sci/ - Science & Math

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5379192 No.5379192 [Reply] [Original]

Doesn't a pendulum contradict conservation of momentum?

>> No.5379195

No. Nothing does. Why do you think so?

>> No.5379199

No it doesn't

>> No.5379203

>>5379195
I think he means, because it changes it momentum all the time

>> No.5379210

>>5379203
It swashes between potential and kinetic energy. But the entire system will of course still conserve momentum.

>> No.5379211 [DELETED] 

conservation of momentum only applies to isolated systems
A pendulum isn't isolated because it is affected by gravity

>> No.5379213

>>5379203
>Implying implications
He only means to troll and his question has been answered twice

>> No.5379217

you have to ask yourself why the pendulum swings at all, if you would do this in a vacuum and without gravity, the pendulim would keep on moving in the same direction, or in a circle around what it's bound to

the pendulum is pulled down by gravity, and thus pulls the earth up by gravity at the same time, thus the momentum here is conserved, also the pendulum will stop swinging at some time because it lost energy/momentum due to air friction

>> No.5379219

>>5379203
I'm terrible at physics but isn't momentum one type of energy or something? Kenetic I assume.

It conserves its energy. Its all potential at the top. I've only seen momentum applies to collisions and shit, but yeah now that OP brings it up I am a bit confused

>> No.5379230

>>5379217
also the pendulum pulls the rope with the same amount the rope pulls the ball

>>5379219
energy isn't a vector quantity as far as I know (not sure about that), while momentum definitly is a vector quantity (it has a direction), the reason why gravity doesn't violate this rule, is because the accelaretion, and thus change of the momentum, point into the exact opposite direction, thus the momentum in the system remains the same

>> No.5379235

>>5379217
It pulls the earth up?

>> No.5379236

>>5379219
also the energy is conserved because kinetic energy and potential energy are transformed into each other, also the reason why gravity does not violate that rule, because it transforms potential energy into kinetic energy

>> No.5379244

>>5379235
ofcourse it does, that's the reason why we circle around the sun, but also pull the sun gets pulled by the same amount towards us, actio et reactio

the reason why we tides is that the moon circels around the earth and the earth gets pulled an equal amount (especially the water)

>> No.5379248

>>5379244
, but also the sun*
why we have*
damn, am quite dyslexic today

>> No.5379268

A lot of people are close, but incomplete with their answers.

Momentum is conserved when there is no external force acting on a system (for us this is the pendulum). Gravity is an external force applying an impulse (change in momentum) to the pendulum. As the other people said, what happens is the kinetic energy (proportional to (p^2)/2m ) is converted to potential energy (roughly mg*(change in height) if the change in height is small and you're not in a weird part of the universe).

Momentum conservation is most useful to think about in collisions. While some more advanced stuff can demonstrate momentum conservation in single particle systems moving in various potentials, it's more useful for a beginner to think of energy conservation in single particle systems, to avoid confusion while building your intuition.

>> No.5379349

>>5379268
>Gravity is an external force

Isn't it accounted for in a pendulum-bob system? By the equation <span class="math">T=2\pi\sqrt{\frac{l}{g}}[/spoiler] or are you talking about the force due to gravity?

>> No.5379443

There's an external force (gravity) acting on the system, so momentum is NOT conserved. This should be obvious guys, conservation of momentum (in Newtonian mechanics at least) comes from setting the external forces equal to zero in Newton's second law:

<div class="math">F=\frac{dp}{dt}=0 ~~\Rightarrow~~ p=const.</div>

More formally, momentum conservation comes from translational invariance in the Lagrangian:

<div class="math">L(q)=L(q+\delta q)</div>

In your pendulum example, the Lagrangian for the system is:

<div class="math">L=\frac{1}{2}mr^2\dot{\theta}^2-mgr(1-cos\theta )</div>

Since <span class="math">\partial L/ \partial \theta\neq 0[/spoiler], the angular momentum of the system (and therefore the linear momentum) is not conserved.

>> No.5379461

Conservation of momentum for a system only applies when no external net torques affect the system.

When the pendulum swings however, in the big picture, there is conservation of momentum due to earths rotation being slowed and sped up by such a small amout that momentum for the system of the earth and the pendulum is conserved since no net external torques work on the system.

> i have been bamboozled

>> No.5379470

>>5379461

Ain't life grand?

>> No.5379485

>>5379443
That's not a closed system. Rewrite it with one and you'll get a Noether current for momentum.

>> No.5379519

>>5379443

Now that you meantion Noether's theorem and conservation laws. There is not a theorem that tells you how many conserved quantities a system has, right? I was reading about the restricted circular three body problem and that there is only one KNOWN constant of motion (jacobi integral), but can you prove that it is the only one?

>> No.5379538

>>5379485
No shit Sherlock.

>>5379519
That's an interesting question, and I have no idea what the answer is.

>> No.5379595

>>5379538
>No shit Sherlock.
Then why TeX all of that up when it's just as obvious? It was already mentioned in here. lel