Mass and angular momentum, left ambiguous by Einstein, get defined • Hacker News Board

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#61

Post by ridiculous_fish » Sat, Jul 16, 2022, 12:37 AM UTC

hinkley wrote: post #7

Maybe a year ago, possibly here, I finally saw gyroscopic precession demonstrated in a way that didn’t invoke magic thinking. The person simply pointed out that the mistake is in thinking of the rotating mass as a stationary object, when in fact you are applying the lateral force to a different spot on the object at each time interval, leading to very strange vectors.

Here's an insight that helped me: gyroscopic precession is the rotational analog of a circular orbit.

A circular orbit is when a linear force is applied orthogonal to linear velocity. The direction changes, but not magnitude (speed).

Gyroscopic precession is when a rotational force (torque) is applied orthogonal to rotational velocity. The axis of rotation changes but not magnitude (rotational speed).

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#62

Post by derefr » Sat, Jul 16, 2022, 12:44 AM UTC

uoaei wrote: post #59

atwood22 wrote: post #56

Earlier quoted context omitted.

That seems like it would violate the conservation of energy. If all the momentum was linear, than changing the direction of those individual particles would require a force.

There are forces holding atoms together, such that the conglomerate constitutes a solid object whose geometry is stable in time. Those forces are strong, and are often sufficient to keep a solid object in the same shape even if rotating at high speeds. Sometimes they are not, in which case the solid object is deformed as the individual atoms are "flung outward" by the (ultimately linear) momentum, which overcomes the…

Thought experiment: if you have an elastic band floating in space, and you nudge it repeatedly to get it rotating faster and faster, will it stretch out (the way a timing belt would if run too fast) or will it stay slack? In its own reference frame, is the band being put under tension — and so experiencing elastic deformation — from the momentum of the particles within it?

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#63

Post by Schroedingersat » Sat, Jul 16, 2022, 12:51 AM UTC

colordrops wrote: post #52

From a layman's perspevtive I've never understood the existence of angular momentum as anything other than a mental model or abstraction. My intuition tells me that all momentum is only linear (except maybe at the fundamental particle level), and perceived rotation is really just a huge amount of linear interactions by individual particles that make up a larger object. This is similar to how a gas is not really a sin…

It's very decidedly not an abstraction on linear momentum.

It's a conserved quantity just like any other. Light has angular momentum even when travelling in a straight line. Anything with spin does even when stopped.

In physics there is a concept known as symmetry. Any way you can swap around your variables without influencing the answers corresponds to a way in which the laws of physics are symmetric (or a way someone could change the time/position/orientation/etc of the region in which you did your experiment and you would get the same results as long as you stayed in the lab they moved).

Angular momentum is the conserved quantity from rotational symmetry and is just as primary as energy-momentum or charge.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#64

Post by Schroedingersat » Sat, Jul 16, 2022, 12:54 AM UTC

atwood22 wrote: post #56

colordrops wrote: post #52

From a layman's perspevtive I've never understood the existence of angular momentum as anything other than a mental model or abstraction. My intuition tells me that all momentum is only linear (except maybe at the fundamental particle level), and perceived rotation is really just a huge amount of linear interactions by individual particles that make up a larger object. This is similar to how a gas is not really a sin…

That seems like it would violate the conservation of energy. If all the momentum was linear, than changing the direction of those individual particles would require a force.

Changing linear momentum does require a force (but not necessarily work), as does changing angular momentum. In orbits it's gravity, in particle interactions it's the electromagnetic force.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#65

Post by mlsu » Sat, Jul 16, 2022, 12:59 AM UTC

atwood22 wrote: post #56

colordrops wrote: post #52

From a layman's perspevtive I've never understood the existence of angular momentum as anything other than a mental model or abstraction. My intuition tells me that all momentum is only linear (except maybe at the fundamental particle level), and perceived rotation is really just a huge amount of linear interactions by individual particles that make up a larger object. This is similar to how a gas is not really a sin…

That seems like it would violate the conservation of energy. If all the momentum was linear, than changing the direction of those individual particles would require a force.

Well, if it completes a full rotation, the applied force over the time of the full rotation is zero (hence, work is zero). So yes, the momentum is linear, but it all pencils out by the direction, right?

That's my understanding of this, but I'm far from a physics expert.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#66

Post by Schroedingersat » Sat, Jul 16, 2022, 1:00 AM UTC

codethief wrote: post #8

shadowgovt wrote: post #2

The most eye-opening thing I've learned about relativity in the past few years is that the notion that space has no preferential direction is an axiom in the theory. There's nothing about the way we measure the speed of light that would disambiguate if light traveled instantaneously in one direction and at half the measured speed of light in the other. We just don't have a way to know, because time measurements requi…

> But it's an axiom. I don't agree. If light traveled instantaneously in one direction, then if we looked in the opposite direction (where such light originates from) we would be seeing stars and galaxies at much more recent time (now). Also, their light would have traveled a much longer distance (due to the ongoing expansion of space) and so would be redshifted much more. All in all what we see on the sky would look…

You can change other things to get the same result.

You can build a consistent theory of aether by asserting that everything (including you) doppler shifts just so and there is a 0 speed through the aether. You get a complicated theory that is not experimentally distinguishable and is incredibly difficult to use and noone would have any idea how to extend to QM or gravity because it's so cumbersome, but it's consistent and mechanics works.

You could easily reframe the frame of reference in such a theory where the lab is moving at 0.999c absolute (which exists in this theory despite being immeasurable) as light moving very slowly in one direction and near instantly in the other.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#67

Post by db48x » Sat, Jul 16, 2022, 1:06 AM UTC

gnramires wrote: post #14

qsdf38100 wrote: post #4

Earlier quoted context omitted.

Veritasium has a nice video about it on YouTube. We can only measure the average back and forth speed of light.

I'm not sure that claim is true. Take this experiment, where A sends B a message following two paths: /-->--B (/ and \ are mirrors) | | | | \-- with speeds: (assume lengths are all 1m) /--cr--B | | cu cu | | \--cl--A The time it takes for path 1 (left,up,right) is cl+cu+cr. The time it takes for path 2 is cu. B can measure the difference cl+cu+cr-cu = cl+cr. A can compare cl+cr to cu: if cl+cr != 2cu the velocity is…

Correct, cl+cr = 2cu is the best you can measure. But it doesn’t follow that cl = cr! Assume a linear transformation like αcl+βcr = 2cu, where α and β tell you how the speed of light varies in between left and right. We simply assume that α = β = 1.0, but what if α=½ and β=³⁄₂? Or α=2 and β=0? A long as α + β = 2.0, then everything will look exactly the same.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#68

Post by yongjik » Sat, Jul 16, 2022, 1:06 AM UTC

derefr wrote: post #62

uoaei wrote: post #59

Earlier quoted context omitted.

There are forces holding atoms together, such that the conglomerate constitutes a solid object whose geometry is stable in time. Those forces are strong, and are often sufficient to keep a solid object in the same shape even if rotating at high speeds. Sometimes they are not, in which case the solid object is deformed as the individual atoms are "flung outward" by the (ultimately linear) momentum, which overcomes the…

Thought experiment: if you have an elastic band floating in space, and you nudge it repeatedly to get it rotating faster and faster, will it stretch out (the way a timing belt would if run too fast) or will it stay slack? In its own reference frame, is the band being put under tension — and so experiencing elastic deformation — from the momentum of the particles within it?

Yes it will stretch out.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#69

Post by lucideer » Sat, Jul 16, 2022, 1:11 AM UTC

leephillips wrote: post #42

hinkley wrote: post #7

Maybe a year ago, possibly here, I finally saw gyroscopic precession demonstrated in a way that didn’t invoke magic thinking. The person simply pointed out that the mistake is in thinking of the rotating mass as a stationary object, when in fact you are applying the lateral force to a different spot on the object at each time interval, leading to very strange vectors.

Does this have something to do with the article? I don’t recall any “magic thinking” in the explanation of precession in my introductory undergraduate physics text. Just Newton’s laws and vector cross-products. “you are applying the lateral force to a different spot on the object at each time interval” : how is that applied when the force is gravity, applied to every point of the object at every time?

> how is that applied when the force is gravity, applied to every point of the object at every time?

It's about the point of suspension resisting gravity. The axis is "held" at a point, applying an "upward" force (resisting gravity). With gravity as you say evenly acting, the point opposite that through the centre of gravity will have a downward vector. The natural result of these opposing vectors might be rotation through the centre of gravity, but when those rotational forces are applied to moving targets you get suspension from the product.

Re: Mass and angular momentum, left ambiguous by Einstein, get defined

#70

Post by kergonath » Sat, Jul 16, 2022, 1:12 AM UTC

colordrops wrote: post #52

From a layman's perspevtive I've never understood the existence of angular momentum as anything other than a mental model or abstraction. My intuition tells me that all momentum is only linear (except maybe at the fundamental particle level), and perceived rotation is really just a huge amount of linear interactions by individual particles that make up a larger object. This is similar to how a gas is not really a sin…

From a layman’s perspective, if something spins, you need to apply a force to it to stop spinning, otherwise it will just keep spinning. Hence, conservation of angular momentum. If you change the mass distribution, it will spin faster or slower, just like ice skaters (this is probably the most striking example), but the angular momentum is still conserved, regardless their linear momentum. There is no fundamental difference between this and what happens at the atomic scale.

The not layman’s answer is Noether’s theorem: the invariance of the laws of physics after a rotation of the frame of reference implies conservation of angular momentum.