Does every object rotate around its center of gravity?

[John Mcrain]

It is said that rocket,plane rotate about center of gravity ,why this is is not case for boats?
Boat pivot point is not in center of gravity.

 

[A.T.]

It is said that rocket,plane rotate about center of gravity , why this is is not case for boats?

See this thread:
https://www.physicsforums.com/threa...bout-their-centre-of-mass.990571/post-6357997

 

[jbriggs444]

Also, boats have keels, daggerboards and centerboards.

 

[anorlunda]

The picture shows the AC75 racing boat. The whole purpose of that foil into move the center of rotation outside the hull. The boat lifts out of the water as it rotates around that point at the end of the foil. You must consider all forces, not just gravity.

 

[John Mcrain]

Also, boats have keels, daggerboards and centerboards.

What do you want to say by this?
Plane also has rudder,wings,flaps,slats,horizontal stablizer etc etc...

 

[jbriggs444]

What do you want to say by this?
Plane also has rudder,wings,flaps,slats,horizontal stablizer etc etc...

For this reason, planes can be regarded as pitching about a horizontal axis through the wings. And sailboats can be regarded as yawing about a vertical axis through the centerboard.

A relevant point is that the center of buoyancy/lift/pressure/whatever has little to do with the center of mass and much to do with the geometry of the shell.

 

[John Mcrain]

For this reason, planes can be regarded as pitching about a horizontal axis through the wings. And sailboats can be regarded as yawing about a vertical axis through the centerboard.

I don't understand your point.
Does rocket, plane rotate around CG?
Only difference in air and water is fluid density,why then boat don't rotate around CG too?

 

[jbriggs444]

I don't understand your point.
Does rocket, plane rotate around CG?
Only difference in air and water is fluid density,why then boat don't rotate around CG too?

I do not understand your confusion.

Much of the question is psychological -- if we describe the motion of an object, we can describe it as a translation and a rotation. We pick a point on the body and ask how that point translates. Then we ask how the rest of the body rotates about that point.

There are many choices about which point to use. Any of them will work. All of them will yield a correct description of the motion of the body. Which should we choose?

Water is key to the successful operation of a boat.

If a boat is purely rotating and not moving then the choice is easy. Pick the point that is stationary in the water. This will be where the centerboard is located. The boat spins in place about its centerboard.

If the boat is purely translating and not rotating then the choice is irrelevant. Any point will do. There is no rotation to worry about.

If the boat is turning while moving then we have a choice. But we want to pick a point that is not moving sideways in the water due to the rotation. That means a point at the centerboard. Any point fore or aft of that would be moving sideways in the water due to the turn. Any point port or starboard of the centerboard could be used -- it does not matter much.

 

[A.T.]

Does rocket, plane rotate around CG?

It's up to you. A plane flying a looping can be described in different ways:
1) Plane's CG moves around the center of the looping & plane rotates around its CG
2) Plane rotates around the center of the looping

 

[John Mcrain]

It's up to you. A plane flying a looping can be described in different ways:
1) Plane's CG moves around the center of the looping & plane rotates around its CG
2) Plane rotates around the center of the looping

Why then center of pressure must be behind CG to have stable rocket?
This is exmple that rocket pivot point is at CG?

 

[jbriggs444]

Why then center of pressure must be behind CG to have stable rocket?

The point you pick for center of rotation has nothing to do with the question you now ask. The rotation rate of the rocket does not depend on one's choice of reference point.

Accordingly, one is free to pick a reference point that makes for an easy explanation.

Since the rocket as a whole may be accelerating, it is convenient to place the reference axis at the center of mass so that any acceleration of the body as a whole has no effect on angular momentum assessed about that axis. Then one can simply ask: "as the object rotates clockwise, does the clockwise torque increase or decrease as a result".

 

[John Mcrain]

it is convenient to place the reference axis at the center of mass

If you put CG behind center of pressure,rocket will be unstable and crash..So it seems CG is real pivot point for rocket,not just math agreement.
Isnt it?

 

[A.T.]

If you put CG behind center of pressure,rocket will be unstable and crash..So it seems CG is real pivot point for rocket,not just math agreement.

The torque around CG determines whether the rocket starts rotating. But that rotation doesn't have a specific "pivot", it's just a change in orientation.

 

[John Mcrain]

The torque around CG determines whether the rocket starts rotating. But that rotation doesn't have a specific "pivot", it's just a change in orientation.

I find here some answers,where people has same confusion as I:

https://physics.stackexchange.com/q...t-pushed-by-multiple-forces?noredirect=1&lq=1

https://physics.stackexchange.com/q...rotate-around-the-torque-vector-or-its-center

https://physics.stackexchange.com/questions/147870/will-an-object-rotate-when-we-apply-a-force-to-it
The rules of motion lead us the following equivalent statements that are valid for both 2D and 3D bodies:

1. A pure force thorugh the center of gravity (with no net torque) will purely translate a rigid body (any point on the body).
2. A pure torque any point on the body (with no net force) will purely rotate a rigid body about its center of gravity

• Every body has a Centre of Mass, whatever its form. If an object has a regular shape and uniform, homogeneous distribution of mass its CoM coincides with its centre.
• If an object is fixed to a pivot, a fulcrum the axis of rotation will be at the pivot
• If an object is free, not fixed to an artificial axis of rotation any action outside the CoM will make it rotate around it

• Suppose now we have an object B (a board, for example, or a door, like in your other question. Its CoM lays at the middle: if we exert a force, an impulse, an impact bang on the CoM, the whole board will move in the same direction.
• If you apply a force on any point except the Com, let's say at one edge, you must specify if the force is rotating with the body. The body will rotate anyway, but if the force always act in the same direction, after a short time it will lose contact with the board.
• Lastly, if a stone, a point mass hits the edge of the board it will move forward and rotate at the same time. Supposing that the projectile has mass 1 and v 20 (p = 20, L = 10, E = 200) and the board has m = 9 and that the collision is elastic, the ball will bounce back at roughly v = -10 m/s , the board will translate at 3.33 m/s and the board will rotate with a frequency ν=2.6rps

 

[hutchphd]

A rigid object set rotating in space far from other influences will rotate about its center of mass. If other "forces" are present it may not.

 

[John Mcrain]

A rigid object set rotating in space far from other influences will rotate about its center of mass. If other "forces" are present it may not.

When gust of side wind hit rocket , will rocket start rotation about CG?

 

[jbriggs444]

A rigid object set rotating in space far from other influences will rotate about its center of mass. If other "forces" are present it may not.

The instantaneous center of rotation of a rigid object can be pretty much anywhere. Pick a frame. Any frame.

The center of mass and a frame where the object is not translating is a useful choice because it means that the instantaneous center of rotation will not be gyrating along a spiral path.

 

[russ_watters]

When gust of side wind hit rocket , will rocket start rotation about CG?

There is no single answer. It may or may not rotate, in either direction...and if it does, you get to pick the point it rotates about.

 

[jbriggs444]

There is no single answer. It may or may not rotate, in either direction...and if it does, you get to pick the point it rotates about.

Regardless of the choice, the change in orientation of the object is an invariant fact of the matter. It does not depend on which choice you make. [Which I know is what you just got done saying]

 

[russ_watters]

Regardless of the choice, the change in orientation of the object is an invariant fact of the matter. It does not depend on which choice you make. [Which I know is what you just got done saying]

Yes, I didn't mean to imply otherwise. I was mostly trying to say that what happens depends on the specifics of the scenario. I can imagine scenarios where a rocket might rotate toward or away from a wind or not at all.

 

[John Mcrain]

The instantaneous center of rotation of a rigid object can be pretty much anywhere. Pick a frame. Any frame.

I really don't understand your "mathematical thinking".I am to stupid to understand this abstract thinking..

 

[John Mcrain]

The instantaneous center of rotation of a rigid object can be pretty much anywhere. Pick a frame. Any frame.

The center of mass and a frame where the object is not translating is a useful choice because it means that the instantaneous center of rotation will not be gyrating along a spiral path.

If I ask you about what point weather vane rotate,what will be your answer?

1)about pivot point rod
2)earth
3)sun
4)galaxy
5)any point

and what answer has the most physics importnace for human that look at this weather vane?

 

[hutchphd]

The center of mass. But of course this is not simple:

 

[etotheipi]

The point is that, under a carefully chosen time-dependent transformation involving a boost and rotation of your coordinates, the rigid body can be made to perform any possible motion.

Anyway, suppose you did settle on a particular frame. Now, select any point $\mathcal{O}$ at $\mathbf{x}_{\mathcal{O}}$ on the body, and let's consider how the position of another point $\mathcal{P}$ at $\mathbf{x}_{\mathcal{P}}$ on the rigid body changes between times $t$ and $t + \delta t$. The point $\mathcal{O}$ undergoes a translation $\mathcal{O}(t+\delta t) - \mathcal{O}(t) = \delta \mathbf{x}_{\mathcal{O}}$, and the change in the position of $\mathcal{P}$, i.e. $\mathcal{P}(t+\delta t) - \mathcal{P}(t) = \delta \mathbf{x}_{\mathcal{P}}$, can be described by compounding the translation $\delta \mathbf{x}_{\mathcal{O}}$ with a rotation by $\delta \phi$ about an axis $\mathbf{n}$ passing through the new position of $\mathcal{O}$, i.e.$$\delta \mathbf{x}_{\mathcal{P}} = \delta \mathbf{x}_{\mathcal{O}} + \delta \phi \mathbf{n} \times (\mathbf{x}_{\mathcal{P}} - \mathbf{x}_{\mathcal{O}})$$Use the Physicist's trick of dividing by $\delta t$,$$\frac{\delta \mathbf{x}_{\mathcal{P}}}{\delta t} = \frac{\delta \mathbf{x}_{\mathcal{O}}}{\delta t} + \frac{\delta \phi \mathbf{n}}{\delta t} \times (\mathbf{x}_{\mathcal{P}} - \mathbf{x}_{\mathcal{O}}) \implies \dot{\mathbf{x}}_{\mathcal{P}} = \dot{\mathbf{x}}_{\mathcal{O}} + \boldsymbol{\omega} \times (\mathbf{x}_{\mathcal{P}} - \mathbf{x}_{\mathcal{O}})$$As it turns out, the point $\mathcal{O}$ that we chose need not even be "on" the rigid body, the only requirement is that it is fixed with respect to the rigid body. Furthermore, you can show (try it!) that whichever such point $\mathcal{O}$ you choose, we get the same angular velocity vector $\boldsymbol{\omega}$. To actually solve mechanics problems, you either take $\mathcal{O}$ to be the centre of mass [for general motion], or the point on the body fixed in the lab frame [for pure rotation].

You can also choose a particular point $\tilde{\mathcal{O}}$ such that the transformation between $t$ and $t + \delta t$ is carried about purely the rotation $\delta \phi \mathbf{n} \times (\mathbf{x}_{\mathcal{P}} - \mathbf{x}_{\tilde{\mathcal{O}}})$, i.e. with $\delta \mathbf{x}_{\tilde{\mathcal{O}}} = 0$; this is the instantaneous centre of rotation. [Although, for motion with no rotation, this will be at infinity...]

 

[jbriggs444]

If I ask you about what point weather vane rotate,what will be your answer?

1)about pivot point rod
2)earth
3)sun
4)galaxy
5)any point

and what answer has the most physics importnace for human that look at this weather vane?

The pivot point is convenient because that is the point that will remain stationary in the ground frame. In this case, the center of mass choice is inconvenient because it would be gyrating in such a frame.

Nonetheless, one can do physics in any frame of reference. Some choices simplify calculations. Some choices complicate them.

 

[John Mcrain]

Nonetheless, one can do physics in any frame of reference. Some choices simplify calculations. Some choices complicate them.

But if you know that weather vane is rotating around pivot point rod,then you know you mast design rear plate behind pivot rod, so arrow will pointing into wind.
If you look that this weather vane rotate about some galaxy,what you useful know for design purpose?

 

[jbriggs444]

But if you know that weather vane is rotating around pivot point rod,then you know you mast design rear plate behind so arrow will pointing into wind.
If you look that this weather vane rotate about some galaxy,what you useful know for design purpose?

It is the same weather vane regardless of what axis you choose to use for the analysis. It changes its orientation by the same amount regardless of what pair of body-fixed points you choose to use to measure deflection. If one does the analysis either way, the result will still come out predicting that that the center of pressure will equilibriate downwind from the mast.

I've already agreed with you that the position of the mast is a convenient choice for the "rotation axis". [It follows naturally from choosing to work in the ground frame]. What more do you wish?

I'm will not say that the weather vane "really" rotates about the mast because the norm is to reserve "real" as an adjective for things that are invariant. Not for things that are free choices.

 

[John Mcrain]

I'm will not say that the weather vane "really" rotates about the mast because the norm is to reserve "real" as an adjective for things that are invariant. Not for things that are free choices.

Hmm, that type of thinking confuse me...
Because every human can see with his eyes that wheater vane is rotating about mast.
But for sure with imaginary thinking it can be rotate about any point..

 

[russ_watters]

Hmm, that type of thinking confuse me...
Because every human can see with his eyes that wheater vane is rotating about mast.
But for sure with imaginary thinking it can be rotate about any point..

It's a very big mistake to draw such a conclusion about what you see. You're making assumptions that may turn out to be wrong, or are just unstated and may not be agreed upon by all:



...but more to the point that people have been trying to drive home; there are many different choices you can make, and if the math works they are all equally "real".

 

[John Mcrain]

It's a very big mistake to draw such a conclusion about what you see. You're making assumptions that may turn out to be wrong, or are just unstated and may not be agreed upon by all:



...but more to the point that people have been trying to drive home; there are many different choices you can make, and if the math works they are all equally "real".

If we take abstract thinking from side,I come to conslusion that rotation at CG in real life is very rare.
If push stick in space at CG,it will just translate.
If you push stick at one end,it will translate and rotate,but pivot point(position which not change position in space) will be out of CG,can even be at point which is out of stick physical limits..

If we want rotation at CG then we must apply two same force at both ends with opposite direction,equaly distance from CG.

 

[berkeman]

If you push stick at one end,it will translate and rotate,but pivot point(position which not change position in space) will be out of CG,can even be at point which is out of stick physical limits..

That's nonsense. Do you have any videos of objects rotating in the International Space Station?

 

[A.T.]

Because every human can see with his eyes that wheater vane is rotating about mast.

It's not your just eyes, but also your brain doing a lot of interpretation. But the interpretation your brain chooses doesn't have to be unique.

 

[John Mcrain]

It is the same weather vane regardless of what axis you choose to use for the analysis. It changes its orientation by the same amount regardless of what pair of body-fixed points you choose to use to measure deflection. If one does the analysis either way, the result will still come out predicting that that the center of pressure will equilibriate downwind from the mast.

I've already agreed with you that the position of the mast is a convenient choice for the "rotation axis". [It follows naturally from choosing to work in the ground frame]. What more do you wish?

I'm will not say that the weather vane "really" rotates about the mast because the norm is to reserve "real" as an adjective for things that are invariant. Not for things that are free choices.

If I want test aircraft in wind tunnel for wind gust/weather vane effect,where I must placed rod ?
At CG,infront CG,behind CG,at rudder,at propeller...?

 

[Ibix]

If I want test aircraft in wind tunnel for wind gust/weather vane effect,where I must placed attached point?
At CG,infront CG,behind CG,at rudder,at propeller...?

The point that @jbriggs444 is trying to make is that you are conflating two issues here.

The question you are asking in the post I quoted is: where do I attach a string to an object such that the string and the weight produce zero torque. That does have a unique, frame-invariant, answer.

That is not the question you asked originally. That question was which point the plane (or boat) rotates around, and the answer to that is frame dependent. Imagine that I run an axle through the nose of the plane and attach the axle firmly to a wall. Then I hold the plane horizontal and release. It will swing down to hang vertically from its nose (i.e. it will seek the position where the reaction force from the axle and its weight have zero torque, again). But where did the plane rotate around? In the lab frame it rotated about its nose, not its center of gravity. But in the rest frame of the center of gravity of the plane the axle moves and the plane rotates about its center of gravity. Neither description is more real than the other. From the point of view of the lab, though, it's easier to say that the plane rotated about the axle through its nose.

 

[russ_watters]

If I want test aircraft in wind tunnel for wind gust/weather vane effect,where I must placed rod ?
At CG,infront CG,behind CG,at rudder,at propeller...?

Anywhere will do. It's common to see the support under or behind the model.

 

[russ_watters]

The question you are asking in the post I quoted is: where do I attach a string to an object such that the string and the weight produce zero torque. That does have a unique, frame-invariant, answer.

Note also, that in these new questions @John Mcrain , the attachment point you are adding isn't just a point/axis of rotation. It applies a force, so in many cases it changes what happens. It isn't merely a convenient reference point.

 

[russ_watters]

If you push stick at one end,it will translate and rotate,but pivot point(position which not change position in space) will be out of CG,can even be at point which is out of stick physical limits..

If we want rotation at CG then we must apply two same force at both ends with opposite direction,equaly distance from CG.

That's nonsense. Do you have any videos of objects rotating in the International Space Station?

You don't need to be in space to test this, you just need to eliminate the influence of gravity. Set a pen or pencil on a table in front of you, oriented left to right (as opposed to pointing at you). Flick the right end away from you with your finger. It starts to spin and move away from you. Does it move straight away or off to the left or right at an angle?

 

[jbriggs444]

As I understand the claim to which @berkeman objected, it was that one can take an object (such as a thin rod) which is initially stationary, apply a momentary impulse at some point within the rod's physical extent and obtain a motion so that the rod has a fixed point (an instantaneous center of rotation) which falls outside the rod's physical extent.

That the rod begins rotating and that its center of mass begins translating, I think we all agree.

That the instantaneous center of rotation will be, at some times, outside the rod's physical extent, I would agree. [1/4 of a rotation after launch, the instantaneous center of rotation will be off to one side of the thin rod]

That the instantaneous center of rotation will be initially outside the rod's physical extent, I would disagree. For a uniform rod and a push at one tip, I seem to recall that the instantaneous center of rotation will be 1/3 of the way from the far end. Testing 5 seconds ago with a handy pen on desktop agrees. By no coincidence, this point is also known as the "sweet spot".

If you have a suitably concave object, one can certainly arrange matters so that the instantaneous center of rotation will initially be outside the object's physical extent. [Imagine a soviet sickle tapped on the handle end]. But for a convex object, I think not.

 

[berkeman]

And even weirder...

 

[A.T.]

As I understand the claim to which @berkeman objected, it was that one can take an object (such as a thin rod) which is initially stationary, apply a momentary impulse at some point within the rod's physical extent and obtain a motion so that the rod has a fixed point (an instantaneous center of rotation) which falls outside the rod's physical extent.
,,,,

That the instantaneous center of rotation will be initially outside the rod's physical extent, I would disagree. For a uniform rod and a push at one tip, I seem to recall that the instantaneous center of rotation will be 1/3 of the way from the far end. Testing 5 seconds ago with a handy pen on desktop agrees. By no coincidence, this point is also known as the "sweet spot".

Okay, but you have constrained to problem from "some point within the rod's physical extent" to "one tip".

 

[jbriggs444]

Okay, but you have constrained to problem from "some point within the rod's physical extent" to "one tip".

Oh, *doh*. You are right. Pushing near the center moves the instantaneous center away from the object.

 

[John Mcrain]

Oh, *doh*. You are right. Pushing near the center moves the instantaneous center away from the object.

Plane fly in wind tunnel test section,not attached to rod,free to move.
If gust hit aircraft from side, and lateral center of pressure is behind CG at fuselage ,then instantaneous center of rotation is somewhere infront CG,using ground as reference frame?

 

[berkeman]

Plane fly in wind tunnel test section,not attached to rod,free to move.

That sounds scary. Do you have any pictures or links?

 

[Richard R Richard]

Hi @John Mcrain I will respond to the initial point that is discussed in the thread.

The definitions that I will give are very perfectible, but let's just go to the main concept.

The center of mass of an object is an object's own characteristic, that is, of the distribution in space of the different densities of the materials that compose it.

The center of gravity is different because at each point of the object there is an acceleration towards the center of a gravitating object (Sun, earth, moon etc whatever), the sum of that mass by accelerations are forces that create a couple on any point reference. In this way, the center of gravity only coincides with the center of mass when there is a symmetry with respect to the main axes of inertia, we can say it in another way, the sum of these moments with respect to the point chosen as GC must be zero.

Well, but a ship, an airplane, are not only subjected to the force of gravity but also to hydrostatic thrust forces of the environment that surrounds it and to the force of aerodynamic or hydrodynamic friction. Therefore a boat is balanced when the Center of Thrust (the point of application of all external forces) is above the center of gravity, any angular imbalance creates a recuperative torque and the boat does not list. In the rocket (at low altitude) and in airplanes, friction is the force that causes the restoring moment while the center of application of this force is ahead in relation to the velocity vector with respect to the center of gravity.

 

[A.T.]

If gust hit aircraft from side, and lateral center of pressure is behind CG at fuselage, then instantaneous center of rotation is somewhere infront CG,using ground as reference frame?

Yes, and if the center of pressure is moved towards the CG, the instantaneous center of rotation moves towards infinity. Pushing exactly at the CG gives you pure translation, which doesn't have a well defined instantaneous center of rotation.

 

[Dale]

It is said that rocket,plane rotate about center of gravity ,why this is is not case for boats?

Do you have a reference for where this is said?

Plane fly in wind tunnel test section,not attached to rod,free to move.

I don’t think this is right.

I think a lot of the confusion in this thread is just you misunderstanding something you read. It would help if you would cite your sources so that we can have a more focused discussion.

 

[John Mcrain]

Yes, and if the center of pressure is moved towards the CG, the instantaneous center of rotation moves towards infinity. Pushing exactly at the CG gives you pure translation, which doesn't have a well defined instantaneous center of rotation.

Why we need 45 posts to answer what I asked?

What if plane flying in sky,a ground is reference frame,gust hit.
we have translation because of plane velocity over ground, but also have side translation cause by gust hit form side,and plane rotation becuase center of pressure is behind CG.
Where is then instantaneous center of rotation?

 

[John Mcrain]

Do you have a reference for where this is said?

I don’t think this is right.

In every video about rocket or plane stability ,they say it rotate about CG..

I put plane fly in test section ,only to avoid translation of airplane speed over ground.Because I didnt know how to deal with these 3 movement ,translation from speed,translation from gust hit and rotation from gust hit...

 

[PeroK]

In every video about rocket or plane stability ,they say it rotate about CG..

You could generalise this:

Every other point on a body moves relative to the CG.

Now, let's pick another point $P$ on the body:

Every other point on a body moves relative to point $P$.

Those are two ways to consider the overall motion:

1) Consider the motion of the CG, then the motion of the body relative to the CG.

2) Consider the motion of point $P$, then consider the motion of the body relative to point $P$.

Now, if we consider a rigid body rotating with angular frequency $\omega$.

1) Every other point on the body rotates about the CG with angular frequency $\omega$.

2) Every other point on the body rotates about the point $P$ with angular frequency $\omega$.

You can't have one without the other. If P moves relative to the CG, then the CG moves reciprocally relative to P.

 

[A.T.]

Why we need 45 posts to answer what I asked?

Because it took you so long to specify what center of rotation you mean.

What if plane flying in sky,a ground is reference frame,gust hit.
we have translation because of plane velocity over ground, but also have side translation cause by gust hit form side,and plane rotation becuase center of pressure is behind CG.
Where is then instantaneous center of rotation?

In front and upwind of the CM.