Coriolis inertial acceleration

[MPavsic]

I am a self learner. I have a specific question regarding the Coriolis inertial acceleration. If question is already answered on this forum please redirect me there.

As depicted on the picture we have rotating platform and the chain of particles passing across the rotating platform. The particles are having limited degrees of freedom, so they have to rotate together with the platform, during their translation. We have two mass particles (b) and (c) of the chain which are at the same distance from the point (A).

The particle (b) is having velocity (v). On the particle (b) is acting normal acceleration (an/a) relative to axis of the rotation about point (A) with angular velocity (Ω). Due translation and rotation of the particle (b) the Coriolis acceleration (ac) is acting upon the particle. The inertial component (ai) of Coriolis acceleration is acting in the opposite direction with magnitude (-2Ω×v). The same applies to the particle (c).

The Question that I have is: Would we have to apply additional acceleration to the rotating platform or to the velocity of the chain of particles, if we want that the rotation of the platform and the velocity of the chain remain constant? Let assume that the length of the chain outside rotating platform does not affect the acceleration of the chain. And that the axis of the rotating platform is able to float.

 

[jbriggs444]

View attachment 270124
I am a self learner. I have a specific question regarding the Coriolis inertial acceleration. If question is already answered on this forum please redirect me there.

As depicted on the picture we have rotating platform and the chain of particles passing across the rotating platform. The particles are having limited degrees of freedom, so they have to rotate together with the platform, during their translation. We have two mass particles (b) and (c) of the chain which are at the same distance from the point (A).

The particle (b) is having velocity (v). On the particle (b) is acting normal acceleration (an/a) relative to axis of the rotation about point (A) with angular velocity (Ω). Due translation and rotation of the particle (b) the Coriolis acceleration (ac) is acting upon the particle. The inertial component (ai) of Coriolis acceleration is acting in the opposite direction with magnitude (-2Ω×v). The same applies to the particle (c).

The Question that I have is: Would we have to apply additional acceleration to the rotating platform or to the velocity of the chain of particles, if we want that the rotation of the platform and the velocity of the chain remain constant? Let assume that the length of the chain outside rotating platform does not affect the acceleration of the chain. And that the axis of the rotating platform is able to float.

Do we have two particles, a finite chain of particles or an infinite chain of particles where we pay attention only to the finite segment that is on the platform at any given time (and where we ignore the momentum being transferred as particles arrive or depart from the platform).

Guessing at a particular interpretation...

We are dealing with the finite length of chain currently on the platform. The chain runs in a well-lubricated groove in the platform. It feeds through the groove at a constant rate. Obviously, the direction is always along the groove. But which direction that is will change as the platform rotates.

Links are added on the upstream side already matched to the platform's rim speed and to the chain's feed rate. We do not care about the force required to accomplish this. It is an external mechanism outside our control. Links leaving the downstream side are simply discarded. Left to spray in a lovely infinite spiral pattern.

We observe that Coriolis force along the entire length of the chain within the groove acts in the same direction. But since the force on the two halves (arriving and leaving) are equal, there is no net torque about the center axis of the platform.

If the platform is to remain in place, it must be anchored against the net Coriolis force. But no torque is required to keep it spinning.

 

[MPavsic]

Hi jbriggs444,
My wording might not be correct regarding the word inertial.
I meant "infinite chain of particles where we pay attention only to the finite segment that is on the platform at any given time.
The speed of the chain is constant.
I have done an experiment in rotating reference frame (similar to the picture above) showing that "inertial part" of the coriolis force pushed the chain of particles toward the local rotation. I can post the description of the experiment in couple of minutes if you want to.

 

[jbriggs444]

I have done an experiment in rotating reference frame

There is no such thing as doing an experiment within a frame of reference.

A frame of reference is something that you can choose when you analyze an experiment. It is a mental construct, not a physical one.

 

[vanhees71]

Sigh! Not again!

I'm however a bit puzzled which specific problem we are talking about. To answer the question, I'd need to know the detailed experimental setup we are talking about.

 

[MPavsic]

A frame of reference is something that you can choose when you analyze an experiment. It is a mental construct, not a physical one.

I am self learner and not a native English speaker. I am trying to understand what I saw during experiment. I saw that the section of the chain of particles deflected toward the centre of local rotation, as i have tried to depict in the picture above.

 

[jbriggs444]

I am self learner and not a native English speaker. I am trying to understand what I saw during experiment. I saw that the section of the chain of particles deflected toward the centre of local rotation, as i have tried to depict in the picture above.

You have a chain of particles that passes through the center of rotation. How can it deflect toward the center of rotation when it is already there?

 

[MPavsic]

Picture update:

At the point A stands the Omega prime.

 

[A.T.]

Coriolis acceleration (ac) is acting upon the particle. The inertial component (ai) of Coriolis acceleration is acting in the opposite direction

There is only one Coriolis force on the particle (which is an inertial force). The other force is the constraint force that limits the degrees of freedom (which is an interaction force).

 

[vanhees71]

I still don't get the meaning of this figure. Is there a particle in a tube, which is rotating? That would be a standard problem, most easily solved in the rotating frame of reference (or even simpler and equivalent, using generalized coordinates and Hamilton's principle).

 

[MPavsic]

I still don't get the meaning of this figure. Is there a particle in a tube, which is rotating? That would be a standard problem, most easily solved in the rotating frame of reference (or even simpler and equivalent, using generalized coordinates and Hamilton's principle).

The particles are part of infinite chain passing through centre of local rotation. stby I will post the recipe for the experiment.

 

[jbriggs444]

Picture update:
View attachment 270126
At the point A stands the Omega prime.

The addition that I see to the drawing is a label indicating counterclockwise rotation at a rate $\Omega_0$

I do not see how that adds any information. We knew already that the platform was rotating.

As I understand the other labels, we have...

$a_c$ for the acceleration of (points on) the chain. All parts are accelerating northwest (up and left). All parts are moving northeast (up and right).

$a_1$ for the acceleration of (points on) the platform due to the net force of the chain, ignoring centripetal acceleration. The entire platform is being accelerated southeast (down and right) by the net force. The actual acceleration of a point on the platform will, of course, be the net of the acceleration of the platform's center plus the centripetal acceleration associated with the platform's rotation. [We assume uniform rotation, so there is no need to contemplate an Euler force].

$a_{n/o}$ for the acceleration of the entire platform. This is identical to $a_1$.

$c$ a sample point on the chain moving northeast (up and right) away from the center

$b$ a sample point on the chain moving northeast (up and right) toward the center

$A$ a label for the center of the platform.

 

[MPavsic]

Jbriggs444 You got it Right, The platform and chain should be pushed to southeast in my opinion. And with time should circle about some point in space. It is 2D problem.
The Question:
Would we have to apply additional acceleration to the rotating platform or to the velocity of the chain of particles, if we want that the rotation of the platform and the velocity of the chain remain constant?

 

[jbriggs444]

Jbriggs444 You got it Right, The platform and chain should be pushed to southeast in my opinion. And with time should circle about some point in space.

Yes. I agree that if the platform is not anchored on a fixed axle, it will move in a circle about a fixed point. Further, this orbit will be synchronized with the rotation of the platform. The effect is that the platform as depicted will be rotating about a point a little bit northwest southeast of its geometric center.

The Question:
Would we have to apply additional acceleration to the rotating platform or to the velocity of the chain of particles, if we want that the rotation of the platform and the velocity of the chain remain constant?

If the platform were held stationary, this would be an easy question. Everything is nice and steady. No torque is required to keep the platform rotating. No net feed force is required to keep the chain advancing.

With the center offset to the southeast... My judgement is that everything is still symmetric and that no net torque and no net feed force is required.

 

[MPavsic]

The experiment:

It might sound or look bizarre, but the observation is what matters.

Experiment requirements:

• Water pump 1000W of power with huge water flow per second
• Softer garden hose internal fi 20 mm, length approximately. 10m
• Speed of the water inside hose should be between 2 and 3 m/s or higher.

Connect garden hose with the water pump and fill the system with water. Connect the remaining end of water hose to water pump, so the closed loop of weather will be created, inside the water hose and the water pump.

Run the water pump.

Pick up the middle section of the water hose, hold the water hose in front of you with both arms stretched and water hose creating an upward arc above your stretched hands. Make a spin around your vertical axis.

If the the water flow inside the water hose is from left to right, and your spin is to the left then water hose arc will decline toward local rotation – which is your spin.

Repeat the experiment at the same conditions, but the water hose creates an arc downwards. You should observe the same result. The water hose arc will decline toward local rotation – which is your spin.

 

[MPavsic]

Yes. I agree that if the platform is not anchored on a fixed axle, it will move in a circle about a fixed point. Further, this orbit will be synchronized with the rotation of the platform. The effect is that the platform as depicted will be rotating about a point a little bit northwest southeast of its geometric center.

If the platform were held stationary, this would be an easy question. Everything is nice and steady. No torque is required to keep the platform rotating. No net feed force is required to keep the chain advancing.

With the center offset to the southeast... My judgement is that everything is still symmetric and that no net torque and no net feed force is required.

Roger, I am advancing my experiment and now checking if can be used for Reactionless propulsion somehow...

 

[MPavsic]

If the platform were held stationary, this would be an easy question. Everything is nice and steady. No torque is required to keep the platform rotating. No net feed force is required to keep the chain advancing.

With the center offset to the southeast... My judgement is that everything is still symmetric and that no net torque and no net feed force is required.

This is exactly what is mind boggling for me is the acceleration to maintain the rotation and chain velocity necessary or not.
Looking at the Coriolis acceleration it changes the direction not velocity of the particle. In the experiment it pushes the hose acr inward the local rotation. If Changed direction of velocity of the particle is pushing upon something, will be force necessary for particle to continue the push in this case? Is angular momentum conserved or not?

 

[jbriggs444]

This is exactly what is mind boggling for me is the acceleration to maintain the rotation and chain velocity necessary or not.

I do not understand the question.

If the platform is anchored, it can succeed in deflecting the chain without torque, energy or any acceleration of itself.

If the platform is not anchored, it can succeed in deflecting the chain without torque, without energy but with some acceleration of itself.

Where is the mind boggling part?

While this is more complicated than a boy whirling a sling around his head with negligible energy input, it is the same idea -- a force at right angles to an acceleration does no work.

One should note that a stream of water and a chain are different. The chain has an additional constraint on the motion of its constituent particles that the stream lacks.

 

[MPavsic]

I do not understand the question.

If the platform is anchored, it can succeed in deflecting the chain without torque, energy or any acceleration of itself.

If the platform is not anchored, it can succeed in deflecting the chain without torque, without energy but with some acceleration of itself.

I got the same calculating result. The mind boggling part was, if platform is not anchored, will the chain particle be able to push themself and the platform from standing still position. I thought that i am missing something, or do I?

 

[jbriggs444]

I got the same calculating result. The mind boggling part was, if platform is not anchored, will the chain particle be able to push themself and the platform from standing still position.

Standing still? We just agreed that it is moving - orbiting a fixed point. If you want to get it going from a standing start, you'll have to be careful about your initial setup so that the final result ends up as a simple rotation/orbit at the right rate rather than an orbit plus a translation at the wrong rate.

Pushing itself? We have stipulated that an external mechanism is squirting chain particles into the platform. Spraying them in a carefully tuned manner so that they arrive at just the right speed and direction in just the right place.

 

[MPavsic]

Sorry the platform and chain are rotating/moving, but the non anchored platform axis is at time t in stand still position. Yes and the External mechanism is pushing a chain across rotating platform.
Would such imaginary mechanism be able to push the axis of the platform from stand still into a circular motion around fixed point in space.

 

[jbriggs444]

Sorry the platform and chain are rotating/moving, but the non anchored platform axis is at time t in stand still position. Yes and the External mechanism is pushing a chain across rotating platform.
Would such imaginary mechanism be able to push the axis of the platform from stand still into a circular motion around fixed point in space.

If the platform is at a stand-still then it is not rotating. How are you planning to get it started rotating?

If it is at a stand-still then it is not orbiting a fixed point. You may not have carefully chosen your frame of reference.

If the mechanism is imaginary than all that is needed is to imagine it. Have it start the chain moving and have it give the platform an initial spin. Done.

 

[MPavsic]

If the platform is at a stand-still then it is not rotating. How are you planning to get it started rotating?

If it is at a stand-still then it is not orbiting a fixed point. You may not have carefully chosen your frame of reference.

The axis of platform is starting to rotate and the chain is started to move across platform as depicted in the picture, until getting some constant angular velocity of the platform and constant velocity of the chain. What will external observer observe?
-Will the axis start to orbit fixed point other than point A in space?
-When constant angular and linear velocity are riched and the observer stops the rotation of the platform around the point other than point A, will the rotating and translating system continue to seek rotation around fixed point in space other than point A.

 

[jbriggs444]

The axis of platform is starting to rotate and the chain is started to move across platform as depicted in the picture, until getting some constant angular velocity of the platform and constant velocity of the chain. What will external observer observe?
-Will the axis start to orbit fixed point other than point A in space?

The picture does not depict any such thing. So we are left to guess at what scenario you now have in mind.

Guess:

We have a stationary platform. We have a stationary chain. We have an external torque on the platform so the platform (and chain) are starting to spin.

It is a chain, not a stream of water. So it does not separate in the middle. It spins. The external observer sees a platform rotating at an increasing rate about its center of mass.

The platform gets to its design rotation rate and the torque is removed. The chain is still not feeding. It is just sitting there spinning with the platform. The external observer sees this.

This state can persist as long as we desire. There is no torque on the platform from the chain and none from the axle. The platform rotates at its design speed forever.

But now we start accelerating the chain in. The feed mechanism is matching velocity with the platform, so the only force here is an inward compression at the upstream end and/or an outward tension at the downstream end. The chain is pushed or drawn through the channel in the platform. There is no friction with the platform, so the feed force has no direct effect on the platform.

The resulting Coriolis force on the chain starts out small (low chain velocity = low Coriolis force) and grows over time. That means that the platform is subject to a net force whose direction rotates at a fixed rate and whose magnitude increases over time at an approximately linear rate. The velocity of the platform will reflect the most recent (and hence strongest) net force. The result should be a spiral trajectory.

Eventually the design feed rate will be reached. The trajectory will stabilize into a circle. But there will almost certainly have been a net unbalanced force over the ramp-up period for the feed rate. So this orbit will be about a moving point.

 

[MPavsic]

The resulting Coriolis force on the chain starts out small (low chain velocity = low Coriolis force) and grows over time. That means that the platform is subject to a net force whose direction rotates at a fixed rate and whose magnitude increases over time at an approximately linear rate. The velocity of the platform will reflect the most recent (and hence strongest) net force. The result should be a spiral trajectory.

Eventually the design feed rate will be reached. The trajectory will stabilize into a circle. But there will almost certainly have been a net unbalanced force over the ramp-up period for the feed rate. So this orbit will be about a moving point.

This is the explanation that I was looking for.
Thank you @jbriggs444

 

[MPavsic]

Eventually the design feed rate will be reached. The trajectory will stabilize into a circle.

The trajectory of the stabilised circle is sort of like centripetal acceleration about fixed point other than A in space.

 

[jbriggs444]

The trajectory of the stabilised circle is sort of like centripetal acceleration about fixed point other than A in space.

I am being picky here, but space does not have any fixed points. Coordinate systems do. Space does not.

Presumably you would be adopting an inertial frame of reference where the trajectory can be described as motion about a fixed point.

I looked up a relevant formula for the resulting motion in terms of the initial rest frame.

∫ x sin(x) dx = –x cos(x) + sin(x) + c

Where x is the number of radians of rotation during the interval while the chain feed is accelerating uniformly.

 

[MPavsic]

@jbriggs444 Thank you, for superb explanations. My last post was just my another brainstorm flash. The most important for me is your notice written above in translation of my post : " If the platform is to remain in place, it must be anchored against the net Coriolis force. But no torque is required to keep it spinning. "
Maybe the galaxies are accelerating throughout the Universe in this way.

 

[berkeman]

Roger, I am advancing my experiment and now checking if can be used for Reactionless propulsion somehow...

Reactionless drives are on the list of banned topics. This thread is now closed. From the PF Rules link (see INFO at the top of the page):

EMDrive and other reactionless drives
See https://www.physicsforums.com/threads/nasas-em-drive.884753/