Undergrad Reference frames, center of rotation, etc

[jbriggs444]

Car travel in constant radius circle track, is this rigid motion?

EDIT: The quoted passage above has been removed from the post in which it appeared. The next few paragraphs are now unmotivated. So I've spoiler tagged them.

Spoiler

If we are treating the car as a point-like object then it is not rigid motion. If all one has have is a moving point then notions of rigidity or rigid motion are irrelevant.

If we are treating the car as an extended object maybe 2 meters wide by 4 meters long by 1 meter high then we do have rigid motion.

It would be convenient to adopt a frame of reference anchored to the center of the track and view the car as rigidly rotating about that non-translating center.

For this scenario, it is challenging to find other sensible descriptions. But not impossible. We might imagine that this circular track is actually a turntable. We might further imagine that this turntable is placed on the deck of an aircraft carrier with the car parked somewhere on the turntable's rim. We might stipulate that the aircraft carrier is moving forward at a speed which is equal to the tangential velocity of the turntable which is rotating clockwise.

If we adopt a frame of reference where the ocean water is at rest and look for an "instantaneous center of rotation", what center will we find?

We look for a point on the turntable that is at rest in our chosen frame. This will turn out to be a point at the rim of the turntable on the starboard side. That is the "instantaneous center of rotation" of the turntable plus car.

How can you throw wheel/stick in the air and force to not rotate around CoM?

With a wave of paper and pencil. The throwing of the wheel/stick has nothing to do with it.

Rotation about the CoM is not a physical fact of the matter. It is a convenient way of describing the physical motion.

 

[Dale]

Why is not rigid motion?

Because the distance between the primary and the satellite can change. And if they are not both tidally locked then the distance between points on either object also changes.

 

[gen x]

Rotation about the CoM is not a physical fact of the matter. It is a convenient way of describing the physical motion.

If center of rotation can not translate per definition, then this hammer not rotate around com from ground frame. Is this ok?
The only way to make com not translate is to use frame origin in com and let axis fixed to ground, does now hammer rotate around com?

 

[A.T.]

does now hammer rotate around com?

Maybe it's a language problem, but you don't seem to get anything from the answers. You just keep asking the same question, that has been answered dozens of times, in this thread and the previous ones.

It's not wrong to say it rotates around the COM, so just stick to that. You don't need to understand why other rotation centers could be used.

 

[gen x]

Maybe it's a language problem, but you don't seem to get anything from the answers.

It think more is problem what my eyes see when looking at something that rotate about itslef, so I can't understand when you say it rotate around every point.. so I am confused with your mathematical views

 

[A.T.]

I am confused with your mathematical views

The way to clear up that confusion is to learn the math, not endlessly go on about what your eyes see.

Or you just forget about it and stick to the decomposition that seems intuitive to you.

 

[Dale]

If center of rotation can not translate per definition,

The center of rotation certainly can translate.

I can't understand when you say it rotate around every point.

Did you not see the plots that I posted? They show what it means. You can pick any point and decompose the motion as a translation and a rotation about that point. That is what those graphs show.

 

[russ_watters]

How can you throw wheel/stick in the air and force to not rotate around CoM? I think it is impossible to not rotate around com. Isnt it?

I'm a mechanical engineer, so I get it: I sometimes find the physicists' view of things to be pedantic. But you need to recognize that you've selected a reference frame and rotation axis that is convenient and obvious from a practical standpoint -- but that doesn't make it special. No matter how much it feels like it should be.

I'll note, though, that your OP was asking fairly general questions about reference frames, so you should be open to the general answers, not just the intuitive/convenient ones.

 

[russ_watters]

Consider a simple case*: you have an object like a ruler, sitting on a desk. You strike one end horizontally, perpendicular to it. What happens? Per the topic of the thread, what hidden assumptions did you make when describing what happens?

*I think this has been discussed before.

 

[A.T.]

The center of rotation certainly can translate.

@gen x might be referring to the instantaneous centre of rotation:
https://en.wikipedia.org/wiki/Instant_centre_of_rotation

The instantaneous centre of rotation results from one possible decomposition, which is convenient for some purposes. But it's obviously not the same as the center of mass in general, which in turn is convenient for other purposes.

 

[gen x]

Consider a simple case*: you have an object like a ruler, sitting on a desk. You strike one end horizontally, perpendicular to it. What happens? Per the topic of the thread, what hidden assumptions did you make when describing what happens?

My assumption is that the desk is frictionless.

Frame fixed to the table:

After the strike, the center of mass (CoM) of the ruler will move in a straight line because the net force is zero. If the CoM were to move along a curved trajectory, a centripetal force would be required, but since no such force exists in our case, the CoM can only move in a straight line.

The ruler will always rotate only about its CoM, because this is the only point that satisfied case net force is zero. If we chose any other point as the center of rotation, the CoM would have to move along a curved path, which again requires a centripetal force that we do not have. Therefore, rotation about the CoM is the only physically possible solution.

During the strike, I do not know what the trajectory of the CoM will be.


In the reference frame fixed to the ruler, nothing translates or rotates.

 

[Dale]

After the strike, the center of mass (CoM) of the ruler will move in a straight line because the net force is zero. If the CoM were to move along a curved trajectory, a centripetal force would be required, but since no such force exists in our case, the CoM can only move in a straight line.

Yes, this is all correct.

If we chose any other point as the center of rotation, the CoM would have to move along a curved path

This is not correct. The CoM moves along a straight line in any case, regardless of our choice of center of rotation.

If we choose another point as the center of rotation (call it B) then B will not move along a straight line, but B is not the CoM.

which again requires a centripetal force that we do not have

There is a centripetal force acting on B.

Therefore, rotation about the CoM is the only physically possible solution.

This is again, not correct.

 

[gen x]

This is not correct. The CoM moves along a straight line in any case, regardless of our choice of center of rotation.

If we choose another point as the center of rotation (call it B) then B will not move along a straight line, but B is not the CoM.

There is a centripetal force acting on B.

I don't understand.
How you get centripetal force in B, if no force act on ruler after the strike?

 

[Dale]

How you get centripetal force in B, if no force act on ruler after the strike?

Inside the ruler there is tension. As it is spinning the material of the ruler is under stress. The motion tries to pull the ruler apart, and the tension inside the material holds it together.

If you spin the ruler fast enough, or if the ruler is fragile, it is possible for the material to break, those forces to go to zero, and the ruler to fly apart. This happens in turbine blades, sometimes spectacularly.

That tension is highest in the center and decreases as you go further out along the ruler. Because it decreases as you go out, there is a net inwards force at B.

 

[gen x]

Inside the ruler there is tension. As it is spinning the material of the ruler is under stress. The motion tries to pull the ruler apart, and the tension inside the material holds it together.

If you spin the ruler fast enough, or if the ruler is fragile, it is possible for the material to break, those forces to go to zero, and the ruler to fly apart. This happens in turbine blades, sometimes spectacularly.

That tension is highest in the center and decreases as you go further out along the ruler. Because it decreases as you go out, there is a net inwards force at B.

But these forces are internal, how can we mix internal and external forces when anylize system?
Internal forces can't move or rotate object, you can't move car if you push with hands on windshield, because this force cancle at seat.

 

[gen x]

At start of video tennis racket is spinning.
Do you agree that racket is rotate around axle that pass through CoM? I see only this, racket is not rotate around man head( "rotate around any point you want").

 

[A.T.]

Internal forces can't move or rotate object,

Internal forces can't accelerate the CoM of an object, but you are asking about the centripetal force at a different point B:

How you get centripetal force in B, if no force act on ruler after the strike?

Why do you think we need a centripetal force in B in the first place? Because you also assumed that there is ruler material at B that is accelerating? Sure, but the internal forces of the ruler, are external forces to the ruler material at point B (infinitesimal part of the ruler around B), and they are are not balanced there.

As a general note: You are confused about mere kinematics, so you should focus on understanding that part, instead of bringing dynamics into it, to confuse yourself even more.

 

[Dale]

But these forces are internal,

So what? Just because they are internal doesn't mean that they don't exist.

But these forces are internal, how can we mix internal and external forces when anylize system?

The usual way is to redefine your system so that the internal force of interest becomes external. We can place the boundaries of our system anywhere we like, and we can analyze multiple systems. This is the completely standard method of analyzing stresses and strains on material bodies, from turbine blades to cars to bridges to anything else.

Internal forces can't move or rotate object, you can't move car if you push with hands on windshield, because this force cancle at seat.

But internal forces can move internal parts of an object. That is what is happening here. B is an internal part of the ruler. You can place a dot of paint on B and you can watch it move. B is moving in a non-straight path, so we know that there is a non-zero net force on B.

 

[gen x]

Why do you think we need a centripetal force in B in the first place?

Because Dale said that B will not move in straight line, so everything what moves in curve need centripetal

 

[gen x]

The CoM moves along a straight line in any case, regardless of our choice of center of rotation.

If we choose center as B, B is now fixed and everything rotate around B, so how CoM still move in stright line in this anylize?

 

[A.T.]

everything what moves in curve need centripetal

No, not everything, just things that have mass. An abstract point B doesn't have mass. If you mean the material at point B, then read my post #47.

If we choose center as B, B is now fixed and everything rotate around B, so how CoM still move in stright line in this anylize?

Draw some pictures, play around with a ruler, It's not that hard.

 

[gen x]

No, not everything, just things that have mass. An abstract point B doesn't have mass. If you mean the material at point B, then read my post #47.

Draw some pictures, play around with a ruler, It's not that hard.

If I choose one point as center then everything else rotate around that center

Do you suggest any video lecture about my topic?

 

[A.T.]

Do you suggest any video lecture about my topic?

You can start with this video, which shows that any combination of rotation & translation
can be expressed by only a rotation (around a different center):

 

[gen x]

You can start with this video, which shows that any combination of rotation & translation
can be expressed by only a rotation (around a different center):

There is only one center for this rotation that is substitution for rotatio+translation?

 

[jbriggs444]

If we choose center as B, B is now fixed and everything rotate around B, so how CoM still move in stright line in this anylize?

One can choose a center at B without choosing a coordinate system where B is moving along a straight line trajectory at constant speed.

With the center of rotation chosen to be at B, there are still many choices available.

One could choose a non-rotating coordinate system attached to the ground frame. Now we have B moving along a cycloidal path while the rod rotates about B.

One could choose a non-rotating coordinate system attached to the center of mass. Now we have B moving along a circular path while the rod rotates about B in synch with B's motion.

One could choose a non-rotating coordinate system attached to B. Now we have B motionless while the rod rotates about B. However, this is not an inertial coordinate system. If we choose to use it, we may need to introduce a time-varying fictitious inertial force when we account for the dynamics.

One could choose a rotating coordinate system attached to B. Now we have B motionless and the rod motionless. However, this is not an inertial coordinate system. If we choose to use it, we may need to introduce other fictitious inertial forces when we account for the dynamics.

One could choose some other arbitrary coordinate system. Now we have B moving along an arbitrary path with the rod still rotating about B. This will almost certainly be a non-inertial coordinate system requiring fictitious inertial forces to account for the dynamics.

 

[Nugatory]

But these forces are internal, how can we mix internal and external forces when anylize system?

We aren't. We are analyzing the forces acting on a given infinitesimal volume somewhere along the rod, and these are all external to that volume.
You might find it easier to understand if you consider two weights connected by an idealized massless string, rotaing with the weights orbiting the center point. The net force on the string/weight/weight sysem is zero so he CoM moves in a sraight line; the net force on each individual weight is non-zero so they do not move in a straight line.

 

[A.T.]

There is only one center for this rotation that is substitution for rotation+translation?

Pure rotation (translation = 0) is just one example of a substitution. There are infinitely many such substitutions where translation ≠ 0, each with a different center of rotation.

 

[gen x]

Pure rotation (translation = 0) is just one example of a substitution. There are infinitely many such substitutions where translation ≠ 0, each with a different center of rotation.

How can I move object from postion 2 in position 1, with pure rotation if I don't use center of this circle?

 

[Ibix]

How can I move object from postion 2 in position 1, with pure rotation if I don't use center of this circle?
View attachment 368039

Consider a frame where the circle is moving to the right. You still have the same angle change, but the rectangle moves further to the right, so sweeps out the arc of a larger circle.

 

[A.T.]

How can I move object from postion 2 in position 1, with pure rotation if I don't use center of this circle?

I don't think you understood my post #57 at all. So again:

If you choose a specific translation (like translation = 0 meaning pure rotation), then one specific center of rotation follows from that choice.

But you can just as well choose some other translation, and then a different center or rotation follows from that different choice.