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The Forgotten Mystery of Inertia

americanscientist.org

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Re: The Forgotten Mystery of Inertia

#81

Post by mannykannot »

mikeash wrote: post #79
mannykannot wrote: post #78

Earlier quoted context omitted.

I think the phrase "...which will continue until the circular path brings it back down" requires a bit more explanation. At this point, you seem to be switching from treating the rotating ring as a stream of independent particles to being a rigid body, but if you treat it as a rigid body from the start, the first part is no longer obvious. I think that once you establish that angular momentum is a vector quantity tha…

You can imagine each particle being somehow tethered to the center, without any need for the particles to be connected otherwise. You’re totally right that gyroscopes are straightforward if you understand angular velocity as a vector quantity, but it’s not quite so intuitive.

If each particle is only tethered to the center, how does the circle bring it down again? If the tethers are all fixed to one another, we're back to rigidity.

Edit: I'm trying to think of a way to bring in angular momentum without having to derive it in full generality...

Re: The Forgotten Mystery of Inertia

#82

Post by naasking »

evanb wrote: post #47
naasking wrote: post #26

Earlier quoted context omitted.

> This is the greatest level of knowing you can have. If it doesn't answer "why?", then it's incomplete. Perhaps at some point in our explorations of physics there will be axioms we must simply accept, but the gyro isn't it. We should have a reason for its behaviour.

Gyros aren't the axiom, they're a theorem---the axioms are Newton's laws of motion.

Not enough. There's no reason why those can't be further reducible. We've already reduced most of those laws into more fundamental principles via Noether's theorem, for instance.

Re: The Forgotten Mystery of Inertia

#83

Post by dom0 »

KGIII wrote: post #35
dingo_bat wrote: post #10

Maybe I'm wrong but it's wrong to say we don't know how a gyro works. We can accurately and precisely predict the behavior of a gyro, derive the mathematical equations necessary and the model we use is general for all moving objects. This is the greatest level of knowing you can have. Maybe the author meant that a gyro's motion is not intuitive to most humans. That I can agree with. For me, even the fact that my smar…

We can accurately predict lensing well enough to see the impact on particles of light - over billions of miles. We can't explain it. The universe is still full of many mysteries. If we knew the why, we'd stop doing science. Our understanding is incomplete and that's okay. It gives our species something to strive for. Do you really understand particle physics well enough to truly understand how your cell phone works?…

> We used simple machines, long before we understood them.

There are infinitely many examples of this, from metallurgy to rolling bearings to gears (gear reduction has nothing to do with teeths), medicine, astronomy (humans have predicted the motion of the stars for thousands of years), ...

Re: The Forgotten Mystery of Inertia

#84

Post by Ended »

lmm wrote: post #74
Ended wrote: post #64

Earlier quoted context omitted.

>Rotation is inherently about different particles moving at different velocities. This is why there is an absolute reference frame for it: it is defined by these differences, so by reducing them to zero and making every particle in the ball have the same velocity, we can reach the "absolute". Imagine the ball is floating in space, and you are watching things through a camera fixed to the ball. To you, the two dots wi…

But if you were the camera you'd feel a force, or not, right? It's not like being in an elevator in free-fall, where you can't tell whether you're accelerating downwards or sitting still in flat space.

True, but the GP suggested that you can find the absolute reference frame by looking at the relative velocities of the dots (independent of any force measurements).

Re: The Forgotten Mystery of Inertia

#85

Post by JoBrad »

lmm wrote: post #74
Ended wrote: post #64

Earlier quoted context omitted.

>Rotation is inherently about different particles moving at different velocities. This is why there is an absolute reference frame for it: it is defined by these differences, so by reducing them to zero and making every particle in the ball have the same velocity, we can reach the "absolute". Imagine the ball is floating in space, and you are watching things through a camera fixed to the ball. To you, the two dots wi…

But if you were the camera you'd feel a force, or not, right? It's not like being in an elevator in free-fall, where you can't tell whether you're accelerating downwards or sitting still in flat space.

How would you tell whether that force is gravitational or centrifugal?

Re: The Forgotten Mystery of Inertia

#86

Post by lmm »

JoBrad wrote: post #85
lmm wrote: post #74

Earlier quoted context omitted.

But if you were the camera you'd feel a force, or not, right? It's not like being in an elevator in free-fall, where you can't tell whether you're accelerating downwards or sitting still in flat space.

How would you tell whether that force is gravitational or centrifugal?

If it were gravitational there would have to be a mass in the right place to cause it. Maybe you could look at how the force changed as you moved around?

Re: The Forgotten Mystery of Inertia

#87

Post by eru »

sopooneo wrote: post #41

A drunk awakens in a void and finds his arms, legs, in fact all extremities are bing pulled outward by some reverse gravity. It is quite unpleasant. By some strange mechanism he is able to make himself start spinning. At first it is worse: in one direction the reverse gravity increases in effect! So he reverses and is relieved to find that in the other it slowly abates. Though the sweet relief is strange. Because if…

And interesting enough, the universe does have a unique privileged inertial reference frame: that which makes the background radiation look isotropic.

Re: The Forgotten Mystery of Inertia

#88

Post by noonespecial »

madaxe_again wrote: post #66
taneq wrote: post #52

Earlier quoted context omitted.

Sounds like a first year physics question. "Consider a spherical drunk in a frictionless vacuum..."

A perfect spherical drunk, in fact.

...of uniform density.

Although, for us, it was always a spherical chicken.

Re: The Forgotten Mystery of Inertia

#89

Post by rocqua »

continuations wrote: post #5

Is Mach's principle related to equivalence principle? It's so strange that inertia mass just so happens to be exactly the same as gravitational mass. Can Mach's principle and equivalence principle be derived from some more fundamental laws or are they accepted as axioms?

The equivalence principle follows naturally from the geometry of general relativity.

The idea is that mass curves space. In this curved space, a 'straight line' is no longer straight. The upshot of this is that if you are standing still, a 'straight line' would actually mean falling down. By inertia, things want to move in straight lines, so we feel gravity. It is an apparent force like the centrifugal force.

If this talk of straight lines in curved space is confusing, consider what passes for a straight line on the surface of a sphere. It still 'curves'.

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