Do objects always rotate around center of mass?

In summary, objects do not always rotate around their center of mass. While the center of mass is the point where the mass of an object is balanced, rotation can occur around different axes depending on external forces, constraints, and the object's shape. In some cases, an object may rotate around a point that is not its center of mass, especially when influenced by external torques or when part of a system with multiple bodies.
  • #71
nasu said:
And at any instant you can find a reference point O so that VP→ is zero. This point is what they call "instantaneous center of rotation" or "instant center of rotation".
Ah, that is a valid definition. This point may be on or off the object, and it will be different in different reference frames.
 
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  • #72
user079622 said:
So men in video is wrong when he said if you choose any point that is not at cg you will get wrong results?
I did not watch all the video. but he seems to talk about a dynamics problem. When it comes to momentum and KE, the decomposition into rotation and translation works only for the COM. But this has nothing to do with the discussion in this thread.
 
  • #73
Dale said:
Ah, that is a valid definition. This point may be on or off the object, and it will be different in different reference frames.
Yes, it does not have on be on the object. I meant to say this but I forgot.
For a body in pure translation, it is somewhere "at infinite".
 
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  • #74
@Dale

He forgot in my video to calculate mxa in case where net force in non zero?
 
  • #75
user079622 said:
Is any difference if my force is some rocket engine at the end of stik working all the time or if my force is short impulse ,when I hit end of stick with hammer?
In first case we have continous external force in second case just first "second" one hit with external force and after that no external force
Will stick behave the same in both case in free space?
This changes the question. We are no longer talking about the instantaneous center of rotation. Instead, we are talking about the behavior of the stick.

Naturally, two different force patterns will produce two different results.

Possibly you have in mind that a stick with a perpendicular rocket on the end that burns for a very long time will settle down into an accelerating spin. Like a pinwheel. You expect that the limiting motion will be a stick spinning extremely rapidly while the stick as a whole drifts at a small velocity in a direction somewhat spinward of the initial thrust. I expect the same.

A drift velocity arises because the initial thrust goes in the same direction for a long time. As the stick speeds up, subsequent thrusts last for a shorter and shorter time in any given direction. Eventually, it is almost averaging out. I've not done the math to determine whether the drift velocity approaches a limit or increases without bound, but I think it is the sum of an inverse square series which will converge. [Back of the envelope says that the impulse from each half-rotation will scale as a simple inverse. This would seem to be a harmonic series -- divergent. But then we are subtracting out the opposite impulse from the next half-rotation. The difference between the two will be approximately an inverse square. So we have a convergent situation].

Now then, you wonder whether the center of rotation will be at the center of mass.

Yes -- nearly so anyway. But only because we have naturally chosen a frame of reference where the stick's center of mass is motionless.

It is only "nearly so" as long as the rocket is still firing. Because it is firing, the center of mass is accelerating. It is moving in a spiral trajectory about a point that I would consider to be a better choice for a reference axis.
 
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  • #76
user079622 said:
But is instant axis of rotation through CoM?
No, because the instantaneous velocity of the CoM is not zero in the ground frame. Of course you can choose another frame as @jbriggs444 noted.

These are two separate choices:
- You can choose a frame of reference, which determines the instantaneous center of rotation
- For every chosen frame of reference you can choose a rotation center, which determines the decomposition into rotation and translation
 
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  • #77
jbriggs444 said:
This changes the question. We are no longer talking about the instantaneous center of rotation. Instead, we are talking about the behavior of the stick.

Naturally, two different force patterns will produce two different results.
In free space there is no resistance so one hit or const. force will get same result?

when plane is hit by wind, this is not equlibrium case so moment in all points are not the same.
 
  • #78
A.T. said:
No, because the instantaneous velocity of the CoM is not zero in the ground frame.
If plane rotate around com ,then from ground frame com travel in straight line. If plane rotate around any other point ,com will not travel in straight line.

I dont know how to express myself, I know when I spin a ball or frisbee, my eyes see that axis of rotation goes through center, I dont know how you call it, maybe I can call it "apparent pivot point"...
 
  • #81
Dale said:
Yes, that is all good
A.T. say it is not good because c.g. has velocity for ground frame
 
  • #82
user079622 said:
In free space there is no resistance so one hit or const. force will get same result?
If the object is rotating or otherwise moving under that "constant" force, then you will have to specify details about how the force changes to match. It will not usually remain constant in direction, magnitude and point of application when the point of application is moving.
 
  • #83
user079622 said:
If plane rotate around com ,then from ground frame com travel in straight line. If plane rotate around any other point ,com will not travel in straight line.
If a rigid object rotates with angular velocity ##\omega## about one axis then it will rotate with angular velocity ##\omega## about any other axis.

The com travels in a straight line if there is no net force, regardless of rotation.
 
  • #84
Dale said:
If a rigid object rotates with angular velocity ##\omega## about one axis then it will rotate with angular velocity ##\omega## about any other axis.

The com travels in a straight line if there is no net force, regardless of rotation.
Object rotate around com, but com translate in straight line.
Camera is ground frame.

 
  • #85
user079622 said:
Object rotate around com, but com translate in straight line.
Yes. The object also rotates around other points besides the com, but the other points do not translate in a straight line. This was covered also in the thread that @A.T. has linked
 
  • #86
Dale said:
Yes. The object also rotates around other points besides the com, but the other points do not translate in a straight line. This was covered also in the thread that @A.T. has linked
Mathematicaly yes, phyiscly not, com is only position on object where ball inside "centrifugal device"(G-indicator) will stay at the middle.

So if airplane really rotate around axis through c.g. when gust hit him, ball inside g-indicator that is placed at c.g. must stay at the middle.
If plane rotate around any other axis, ball will move to side due to centrifugal force.

But ball will move to side due to downwind translation, because wind accelerate plane slightly downwind, later thurst from engine stop this movement.

Do you agree?

1696609800627.jpeg

So basically my question is; will plane c.g. move in straight line during plane change his orientation when gust of wind hit him?
 
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  • #87
user079622 said:
Mathematicaly yes, phyiscly not, com is only position on object where ball inside "centrifugal device"(G-indicator) will stay at the middle.So basically my question is; will plane c.g. move in straight line during plane change his orientation when gust of wind hit him?
Your first sentence is logically faulty. The special dynamic properties of the COM are completely irelevant to the discussion about the kinematics of the rotationg bodies. The motion of points on the object is what it is. There is no difference between "matematically" and "physically". They either move in a specific way or they don't.

You keep going around in circles (or more like on tangents) where there is nothing to argue about. There is no doubt that objects may and do rotate around the COM. Nobody denied this. But rotation is not an exclusivist club. Rotation around one point does not exclude rotation about any other point. It's not and either/or situation. Do you have same problem with just motion? If the moon moves relative to the Earth will you deny that it also moves relative to Jupiter or the Sun? If someone says that the Moon moves relative to the Sun will you say, "Hey, this should be wrong because Wiki says that it moves relative to the Earth!"?If the plane was already moving before the wind hits, the trajectory of the COM will follow a curve and not a straight line. It si the same as with a rock thrown horizontally and being deviated by gravity.
There is the special case where the plane's COM was already moving in a straight line and the wind direction is exactly along the straight line. But then there will be no change in orientation either.
 
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  • #88
nasu said:
If the plane was already moving before the wind hits the trajectory of the COM will follow a curve and not a straight line. It si the same as with a rock thrown horizontally and being deviated by gravity.
There is the special case where the plane's COM was already moving in a straight line and the wind direction is exactly along the straight line. But then there will be no change in orientation either.
Yes I agree with this, in nature there is not sharp turn, so when plane change his direction that must be done in curve.

But I focus at c.g. only at rotation phase, when he change his orientation into wind...
 
  • #89
user079622 said:
com is only position on object where ball inside "centrifugal device"(G-indicator) will stay at the middle.
That is true regardless of which point you consider the rotation axis.

user079622 said:
So if airplane really rotate around axis through c.g. when gust hit him, ball inside g-indicator that is placed at c.g. must stay at the middle.
If plane rotate around any other axis, ball will move to side due to centrifugal force.
This is simply not true. The choice of rotation axis does not alter the motion of the ball.

user079622 said:
So basically my question is; will plane c.g. move in straight line during plane change his orientation when gust of wind hit him?
No. The net force is not zero, so there will be acceleration. The motion of the com will therefore not be a straight line at a constant speed.
 
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  • #90
user079622 said:
Yes I agree with this, in nature there is not sharp turn, so when plane change his direction that must be done in curve.
This has nothing to do with sharp turns. A gust of wind will not cancell the 500 mph speed of the airplane (including the COM). What happens with a point object moving in a straight line at 500 mph when a force start acting perpendicular to the initial trajectory? Does it move in a straight line? Does it move with constant velocity? If you understand the motion of point like objects, you should understand the motion of the COM. If not, maybe you need to review motion of point-like objects under the action of various forces, before looking at motion of rigid bodies.
 
  • #91
Dale said:
This is simply not true. The choice of rotation axis does not alter the motion of the ball.
Left object rotate around P1, ball in g indicator set at c.g. will move out,
Right object rotate around around c.g. ball will stay in center.

This is what I want to say..
Untitled.png


Dale said:
No. The net force is not zero, so there will be acceleration. The motion of the com will therefore not be a straight line at a constant speed.
Lets assume engine is mount on tail so it cant make any torque around c.g..
In time t1 plane start change direction and change orientation, in time t2 plane settle new direction but still change his orientation toward wind, in time t3 plane is settle his new orientation

Does com travel in straight line from time t2 to t3?

Or I can assume momentum of plane is so high 200tones x high speed, so change in direction due to gust of 60km/h is neglibile, so we can analyze/focus only change in orientation..
 
  • #92
user079622 said:
Does com travel in straight line from time t2 to t3?
Is there a net force from t2 to t3?
 
  • #93
Dale said:
Is there a net force from t2 to t3?
Is possible situation that net force=0 but net moment is non zero due to gust, so plane still changing just orientation?
If yes, then yes net force is zero
 
  • #94
user079622 said:
Left object rotate around P1, ball in g indicator set at c.g. will move out,
Right object rotate around around c.g. ball will stay in center.

This is what I want to say..
Let me make sure that I am clear about the drawing. We have two depictions of the same scenario. In both cases, the rod is rotating at the same rate in the counter-clockwise direction.

In the first case, we place the instantaneous cebter of rotation well out north (toward the top of the page) from the rod. The instantaneous axis of rotation is supposed to be stationary. That means that the frame of reference which you have chosen is one in which the rotating rod is moving rapidly to the east. You might imagine the axis along with its rest frame moving rapidly to the west.

In the second case, we place the instantaneous center of rotation in the center of the rod. That means that the frame of reference which you have chosen is one which moves along with the rod but without rotation. Viewed against this frame, the rod is rotating in place.With this understanding in hand, your point is that the two depictions of the scenario yield physically distinguishable results. In one case there is a force detectable by an accelerometer at the center of mass. In the other case there is not. You conclude from this that one depiction is unambiguously right and the other is unambiguously wrong.

This turns out to be incorrect.

The reason it is incorrect involves what we mean by an "instantaneous center of rotation". It is the center only for an instant. It is not permanent. At any later time, there may be a different point that is the new "instantaneous center of rotation".

Because of this, knowing one "instantaneous center of rotation" plus the rotation rate only allows you to know the velocity of every point on the rigid object. Not their future and past trajectories. Not the curvatures of those trajectories. Not any accelerations.

In the case of the drawing you have provided with the spinning rod moving eastward as it spins counterclockwise about an instantaneous center of rotation to the north, the situation would be like a wheel rolling along a wall to the north. The instantaneous center of rotation would always be due north of the center of mass. The accelerometer would read zero.

Just like an accelerometer on the axle of a wheel on a car driving down the highway.
 
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  • #95
user079622 said:
Is possible situation that net force=0 but net moment is non zero due to gust, so plane still changing just orientation?
If yes, then yes net force is zero
If the net force is zero then the com moves in a straight line. If the net force is not zero then the com does not move on a straight line
 
  • #96
Dale said:
If the net force is zero then the com moves in a straight line. If the net force is not zero then the com does not move on a straight line
When net force =0 must be net moment also zero?for my case
 
  • #97
user079622 said:
When net force =0 must be net moment also zero?
No. The net momentum need not be zero. Nor must the net torque be zero.
 
  • #98
jbriggs444 said:
No. The net momentum need not be zero. Nor must the net torque be zero.
I try to draw forces for my case net force=0 and net moment non zero, but I struggle.
 
  • #99
user079622 said:
Left object rotate around P1, ball in g indicator set at c.g. will move out,
Right object rotate around around c.g. ball will stay in center.

This is what I want to say..View attachment 333162
What you seem to mean is a pivot point that remains at rest in some inertial reference frame. This is very different from purely kinematic centers of rotation, which don't care about the reference frame being inertial.

Also note that if a gust hits a plane, it's CoM will not be inertial, so it's not the pivot you are looking for.
 
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  • #100
A.T. said:
it's CoM will not be inertial,
What does it mean?
A.T. said:
so it's not the pivot you are looking for.

And what pivot I am looking for?
 
  • #101
If I record with camera(connected with earth) plane from top view, plane passes under camera when crosswind hit him.
After I can slow down video, draw line along aircraft in software and find around which point I see rotation.

Let say for this example I find that he rotate around point P.
Yes point P will move on my screen as plane fly,
but distance from P to c.g. will be same all the time..

What is name of this point/axis of rotation?
V5uNb.png
 
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  • #102
Any point at fixed distance from the com satisfies this condition. The plane rotates around it (if there is any rotation) and keeps the same distance from COM. The tip of the pilot's nose will do, as long as he does not move from his seat.
 
  • #103
madisonandhaley said:
I looked up your question on CK-12 and this is what I got:
Yes, objects always rotate around their center of mass. This is because the center of mass is the point at which all of the mass of the object can be considered to be concentrated for the purpose of calculating rotational motion.
I hope this helps!

This answer restates the question IMHO. It seems to imply that objects can be considered point masses for rotational purposes.......which is not true. What is CK-12?
 
  • #104
user079622 said:
I can slow down video, draw line along aircraft in software and find around which point I see rotation.

What is name of this point/axis of rotation?
It's called "the point around which user079622 sees rotation".
 
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  • #105
A.T. said:
It's called "the point around which user079622 sees rotation".
So this is not that instant center? When I stop video at that time this is instant point around plane rotate..
 

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