Undergrad Reference frames, center of rotation, etc

[gen x]

Topic about reference frames, center of rotation, postion of origin etc

Comoving ref. frame is frame that is attached to moving object, does that mean, in that frame translation and rotation of object is zero, because origin and axes(x,y,z) are fixed to object? Is it same if you place origin of frame at object center of mass or at object tail?
What type of comoving frame exist? What is lab frame?


If we talk about center of rotation do we always need to specified from what frame we observe?

 

[A.T.]

Comoving ref. frame is frame that is attached to moving object, does that mean, in that frame translation and rotation of object is zero, because origin and axes(x,y,z) are fixed to object?

You can define it either way. Whatever is more convenient.

If we talk about center of rotation do we always need to specified from what frame we observe?

"Center of rotation" is ambiguous, even if the frame of reference is given, because there are infinitely many ways to decompose a rigid transformation into rotation and translation.

 

[anuttarasammyak]

Suppose the object is rigid. Fixing the positions of any three points on the object is sufficient to construct a co-moving coordinate system. Any frame of reference that remains at rest with the system is also a co-moving coordinate system. Usually, one chooses a frame whose origin is at the center of mass.

 

[Dale]

"Center of rotation" is ambiguous, even if the frame of reference is given, because there are infinitely many way to decompose a rigid transformation into rotation and translation.

To support this see the plots I posted below

This is just a mathematical fact of rigid body motion, purely kinematically. It has nothing to do with forces, just the way that rigid body motion behaves mathematically.

Suppose I have a rigid disk which is spinning about its center of mass. At a given instant I can plot the velocity of each point on the disk as follows:

View attachment 319993
The formula for the velocity field is $\vec v=(y,-x)$. This is rotation around the center, as expected.

However, suppose instead of a disk rotating, we have a wheel rolling. Kinematically these are the same motion in different reference frames. Then at any given instant I can plot the velocity of each point on the wheel as follows:
View attachment 319994
The formula for the velocity field is $\vec v=(y,-x)+(1,0)$. Notice that this motion is also a pure rotation, but about the bottom of the wheel, the point that it contacts the ground. Again, this is kinematically identical to the disk rotating about the center in a different reference frame.

These two points are not special. In fact, for any point on the wheel you can pick a reference frame where that point is momentarily at rest. When you do so the motion is as follows:
View attachment 319996
The formula for this velocity field is $\vec v=(y,-x)+(0,0.7)$. Notice again that this motion is momentarily a pure rotation about the chosen point which happens to be $(0.7,0)$.

This is a general feature of rigid body motion. You can always decompose the velocity of the material points in a rigid body into a pure rotation about any point and a rigid translation.

So again, it isn't that the rotation is about the center of mass, but that the translation of the center of mass is particularly simple.

 

[wrobel]

What is lab frame?

I am afraid this notion is not completely formalized. Say a lab frame is an inertial frame you are sitting in and with respect to which you are observing the motion.
The notion of instantaneous center of rotation is well defined for planar problems of rigid body kinematics. But it is not a part of the minimum needed for problem solving.

 

[gen x]

You can define it either way. Whatever is more convenient.

If origin and axes are fixed to object, then nothing moves, so what I can calculate here? what is point of that frame?

https://www.physicsforums.com/attachments/random-png.319996/

What is purpose of that center, if I put here ball bearing, that wheel cant be driven, because car will jumps(unballance)?
From ground frame wheel of car has instantaneous Center of Rotation at contact patch, from car frame center of rotation is at wheel CoM(ball bearing)?

How to find pivot point for this stick, we know CoM, two forces, stick lay on table, F2 is center of lateral friction force from table surface. F1 and F2 are constant forces, not impulse

 

[wrobel]

It is a very bad idea to throw kinematics and dynamics in the same heap

 

[gen x]

It is a very bad idea to throw kinematics and dynamics in the same heap

how do you mean?

 

[wrobel]

how do you mean?

I mean that one should first study kinematics and after that dynamics.

From ground frame wheel of car has instantaneous Center of Rotation at contact patch, from car frame center of rotation is at wheel CoM(ball bearing)?

Any motion is defined with respect to some frame only. So what?

 

[gen x]

He talk how objects naturally rotate about their Centers of Mass, from wich frame?
Do you agree that object tend to rotate about their Centers of Mass?

​

 

[wrobel]

Do you agree that object tend to rotate about their Centers of Mass?

This phrase does not make sense.

 

[gen x]

This phrase does not make sense.

Why not?

 

[wrobel]

Why not?

provide a definition of the notion "a rigid body rotates about a point"

 

[A.T.]

If origin and axes are fixed to object, then nothing moves, so what I can calculate here? what is point of that frame?

When doing physics on Earth, we usually use a reference frame with origin and axes fixed to the Earth.

Do you agree that object tend to rotate about their Centers of Mass?

Depends on the definition of "to rotate about a point", as already explained above, and in many previous threads:
https://www.physicsforums.com/threa...ays-rotate-about-their-centre-of-mass.990571/
https://www.physicsforums.com/threads/does-every-object-rotate-around-its-center-of-gravity.998359/
https://www.physicsforums.com/threa...-rotate-only-about-its-center-of-mass.986625/
https://www.physicsforums.com/threads/does-the-moon-rotate-on-its-axis.874223/

 

[gen x]

Question:

Why do unconstrained objects always rotate about the lines passing through their CMs when tangential forces are applied to them? I understand that if an object does not rotate about its CM, then its rotation will decay to the rotation about the axis passing through its CM.

Answer:

If they did not then the center of mass would not be traveling in a straight line. This would violate Newton’s first law.

Objects always rotate about the lines passing through their CM is only valid when net force=zero?
But isn't we say that object rotate around any point?

Depends on the definition of "to rotate about a point", as already explained above, and in many previous threads:

Relitivization of the turning point, if that point is relative then we can't say object rotate around that point.

 

[A.T.]

Answer:

Here a more recent and accurate answer by the same poster, already quoted in this thread:

So again, it isn't that the rotation is about the center of mass, but that the translation of the center of mass is particularly simple.

Relitivization of the turning point, if that point is relative then we can't say object rotate around that point.

It's not about being relative in the sense of 'frame dependent'. Even when the frame is given, you can say it rotates about any point, by choosing the matching translation of that point. But as written above, some translations are simpler, and thus more convenient.

 

[anuttarasammyak]

Usually, one chooses a frame whose origin is at the center of mass.

FYI Landau-Lifsitz's Mechanics explains in section 31

Then they investigate the case where O' which is distance a from O is taken. I recommed you to find a copy and read it.

 

[Dale]

What is purpose of that center,

The point is to show that any point can be chosen as the center, if desired. You have freedom to choose the center.

if I put here ball bearing, that wheel cant be driven, because car will jumps(unballance)?

You misunderstand. All of those plots show the same motion of the same object at the same time. In all three plots the axle is in the center of the wheel and the wheel is spinning smoothly. There is no physical difference between the three. The differences are purely mathematical. For the same rigid physical motion you can choose any point and decompose the total motion as a translation and a rotation about that chosen point.

How to find pivot point for this stick

What does it mean for a point to be a pivot point?

Do you agree that object tend to rotate about their Centers of Mass?

I would agree. I would also agree with someone who picked any other point. Rigid objects rotate about any given point at the every time.

Usually, you choose the point that makes the math easiest. Often that is the center of mass.

Objects always rotate about the lines passing through their CM is only valid when net force=zero?
But isn't we say that object rotate around any point?

I did explain that later in the same thread. If you are reading that thread then keep reading. It is a long one.

 

[wrobel]

Eventually understanding is an ability of problem solving and nothing else:)

 

[gen x]

All of those plots show the same motion of the same object at the same time. In all three plots the axle is in the center of the wheel and the wheel is spinning smoothly. There is no physical difference between the three. The differences are purely mathematical.

Can we ask where is physical center of rotation of object, does that make more sense?

 

[Ibix]

Can we ask where is physical center of rotation of object, does that make more sense?

Not really, because the problem is that there are multiple ways to break the motion of a rigid body into rotation and translation, and they all give different answers for where the center of the rotation is. All are equally valid.

Intuitively, you probably want to pick the center of mass frame, and then the rotation is about the center of mass. But you are not obliged to do so.

 

[gen x]

Not really, because the problem is that there are multiple ways to break the motion of a rigid body into rotation and translation, and they all give different answers for where the center of the rotation is. All are equally valid.

Intuitively, you probably want to pick the center of mass frame, and then the rotation is about the center of mass. But you are not obliged to do so.

Does that apply to center of revolution as well?

 

[Dale]

Can we ask where is physical center of rotation of object, does that make more sense?

You can ask “which center of rotation makes my analysis easiest”.

 

[jbriggs444]

Does that apply to center of revolution as well?

I have never encountered the term "center of revolution" in the context of physics. Nor has Google, it seems. The references it found were to politics and war.

Can you explain what you mean by "center of revolution" as distinct from "center of rotation"? Maybe the barycenter of a pair of objects orbiting one another?