Do objects always rotate around center of mass?

[user079622]

For example if airplane or boat move rudder, do they always rotate around center of mass?
Or exist specific conditions when object rotate around center of mass?

 

[Dale]

If I take a disk, nail it to the wall with a nail placed somewhere besides the center of mass, and then spin it, then it will not rotate around the center of mass.

For an airplane or a boat I am not sure if the point they rotate around is well defined.

 

[PeroK]

For example if airplane or boat move rudder, do they always rotate around center of mass?
Or exist specific conditions when object rotate around center of mass?

What's the definition of rotate?

 

[Dullard]

Center of force(s). That may (or may not) be the center of mass.

 

[Halc]

For example if airplane or boat move rudder, do they always rotate around center of mass?

Take an SR-71 blackbird at top speed. When the rudder is turned (OK, there's far more to turning an aircraft than just adjusting the rudder), the aircraft rotates about an axis at least 150 km away from its center of mass, so the answer is no, they don't always rotate about the center of mass.

Similar answer to a boat, but there are boats that can rotate in place using side thrusters. The rudder alone is not up to the task.

 

[Dale]

the aircraft rotates about an axis at least 150 km away from its center of mass,

How do you determine or define that?

 

[A.T.]

For example if airplane or boat move rudder, do they always rotate around center of mass?
Or exist specific conditions when object rotate around center of mass?

We had this question many times already:
https://www.physicsforums.com/threa...bout-their-centre-of-mass.990571/post-6357997

 

[Halc]

How do you determine or define that?

The axis 150 km from the aircraft is the origin of the only rotating reference frame in which the blackbird is reasonably stationary for the duration of the turn.

As for if rotation is about the CoM, it all depends on where you assign the axis of rotation, not obvious given that fact that the objects in the examples are not inertial, but have off-center forces being appied to them.

 

[nasu]

This question is asked quit frequently without actually specifying what does it mean.
For a general motion of a rigid body, there are several questions possible:
1. Is the body rotating about the COM? Very likely that the answer is yes.
2. Is the body rotating ONLY about the center of mass? Definitely no.
3. Is the motion about the COM a pure rotation? Not in general.

For a rigid body we have a general theorem taht says that at any moment, the velocity of any point of the rigid can be written as the velocity (translation) of anoter point plus a rotation around this point. The nice think, al,ost magic, is that not only forr all the points the roatation has the same angular velocity but even if we pick another point, the translation changes but the angular velocity of rotation is the same. So, it looks like the rigid rotates around any point you like.
At any moment, there is a special point which have zero translation so the motion is a pure rotation around this point. This point (instantaneous center of rotation) does not have ot be the COM and in general is not. Actually, in general is not a fixed point on the rigid body, it may change in time.
A very common example is the rolling without slipping of a disk. The instanaeous center of rotation is the contact point, not the COM. The motion of the disk can be described as a pure rotation around this point. But the disk also "rotates" around any other point, including the COM (or the top point of the disk).

The importance of the COM is not in tso much in the kinematics but in the dynamics of the rigid body motion. The decomposition of KE and momentum in translation and rotation without cross terms works only for the COM. But this does not imply that the body rotates only around the COM.

 

[Dale]

it all depends on where you assign the axis of rotation, not obvious given that fact that the objects in the examples are not inertial, but have off-center forces being appied to them

Yes, that is my issue with the question. The answer is not unique.

Even for something like the moon, and even idealized as a perfectly circular tidally locked orbit, you can make a convincing case that it rotates about the barycenter and a convincing case that it rotates around its center of mass. You can even make a (less convincing) case that it rotates about any arbitrary point.

 

[nasu]

Why it is less convincing? It does rotates about any point. In what acception of "rotate" it is less convincing?

 

[Dale]

It is empirically less convincing. I have had discussions where I showed rotation around different points. The center of mass was convincing to them, as was a fixed center of rotation, but other random centers were not so convincing to them.

See this post and the immediate reaction to it
https://www.physicsforums.com/threa...bout-their-centre-of-mass.990571/post-6840284

 

[user079622]

. You can even make a (less convincing) case that it rotates about any arbitrary point.

Then this we call revolve not rotate.

How can moon rotate around any point?

 

[Lnewqban]

For example if airplane or boat move rudder, do they always rotate around center of mass?
Or exist specific conditions when object rotate around center of mass?

Please, see:
https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/aircraft-rotations/

https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/rudder-interactive/

 

[Dale]

Then this we call revolve not rotate.

How can moon rotate around any point?

It is just a mathematical fact of rigid body motion. You can decompose any arbitrary rigid body motion into a rotation about some arbitrary point and some translation.

 

[nasu]

It is empirically less convincing. I have had discussions where I showed rotation around different points. The center of mass was convincing them, as was a fixed center of rotation, but other random centers were not so convincing to them.

See this post and the immediate reaction to it
https://www.physicsforums.com/threa...bout-their-centre-of-mass.990571/post-6840284

Ok, I understand now what you mean by "convincing". Somehow I missed that thread.

 

[nasu]

Then this we call revolve not rotate.

How can moon rotate around any point?

Can you provide a clear definitions showing the difference between the two terms?
Also, what do you mean by "rotate around a point"?

 

[PeroK]

How can moon rotate around any point?

If a rigid body is rotating, then it is rotating with the same angular speed about any point on the body. Imagine being on a carousel. From any point on the carousel, every other point on the carousel is rotating around you.

This is true of any rigid body, as the distance between any two pairs of points is constant owing to the rigidity.

 

[user079622]

It is just a mathematical fact of rigid body motion. You can decompose any arbitrary rigid body motion into a rotation about some arbitrary point and some translation.

Frisbee always rotate around com, however you throw it. And revolve around some other point which is out of his dimensions.

 

[user079622]

If a rigid body is rotating, then it is rotating with the same angular speed about any point on the body. Imagine being on a carousel. From any point on the carousel, every other point on the carousel is rotating around you.

This is true of any rigid body, as the distance between any two pairs of points is constant owing to the rigidity.

But if I accept that some point rotate around me instead that I rotate around center of carousel, then centripetal acceleration is zero, because I am in center. So forces on me is not correct.

 

[PeroK]

Frisbee always rotate around com, however you throw it.

Not all 3D motion is a rotation. More complex motion is possible if the frisbee is subject to external forces.

If the frisbee is not subject to external forces, then the CoM moves inertially and all other points rotate about an axis through the CoM. But, not about the CoM (unless the frisbee is 2D). The Earth, for example, has an axis of rotation, not a single point.

 

[Dale]

Frisbee always rotate around com, however you throw it.

How can you justify that claim? I.e. what makes you uniquely specify the com?

For example, there is a point which is momentarily at rest. The frisbee is momentarily rigidly rotating around an axis through that point. That point is not the com. So what excludes that point?

 

[user079622]

Not all 3D motion is a rotation. More complex motion is possible if the frisbee is subject to external forces.

If the frisbee is not subject to external forces, then the CoM moves inertially and all other points rotate about an axis through the CoM. But, not about the CoM (unless the frisbee is 2D). The Earth, for example, has an axis of rotation, not a single point.

Yes I mean axis that passes through CoM.
What you will say about my post #20 ?

 

[user079622]

How can you justify that claim? I.e. what makes you uniquely specify the com?

For example, there is a point which is momentarily at rest. The frisbee is momentarily rigidly rotating around an axis through that point. That point is not the com. So what excludes that point?

It rotate around axis that passes through center of frisbee

 

[PeroK]

But if I accept that some point rotate around me instead that I rotate around center of carousel, then centripetal acceleration is zero, because I am in center. So forces on me is not correct.

This is a non-inertial frame. But, in that frame, the motion of the rest of the carousel can be described as a rotation about that point. It's sometimes useful to do this. For example, mapping the stars in the night sky from Earth. There is nothing invalid about this just because the Earth is "really rotating". We can work quite happily from a rotating reference frame and map the motion of the stars as a rotation about Earth.

In Newtonian mechanics, inertial reference frames have a special place. But, in General Relativity, the laws of physics are independent of the reference frame. And, indeed, in GR there are no global inertial reference frames in any case.

 

[nasu]

Frisbee always rotate around com, however you throw it. And revolve around some other point which is out of his dimensions.

This discussion will be pointless until you define exactly what do you mean by "rotate". It may be that you have a special meaning or intuition of the term. More specific, what criterion do you use to know that it rotates around COM (or any other point). And even more important, how do you determine that it does not rotate around another point, let say half way between COM and the edge of the fresbee? When you say that it does not rotate around some point, you must have some rule or criterion to say this. What is it?

 

[Dale]

It rotate around axis that passes through center of frisbee

It also rotates around an axis that passes through any other point, as I mentioned above. So that doesn't distinguish the center.

 

[user079622]

It also rotates around an axis that passes through any other point, as I mentioned above. So that doesn't distinguish the center.

So you say crankshaft rotate about any point ?
If rotate around any axis that not passes through center of main bearing , will be in eccenter and engine will vibrate/shake.

 

[Dale]

So you say crankshaft rotate about any point ?
If rotate around any axis that not passes through center of main bearing , will be in eccenter and engine will vibrate/shake.

If it is mounted on any axis that does not pass through the center, it will shake. That is a different statement than what it rotates about.

Frisbees rotate, but they aren’t mounted to anything.

A wheel is mounted to its axle, but it also rotates about the contact point on the ground.

Mounting and rotating are not the same

 

[nasu]

It rotates about any point but only one is the instantaneous center of rotation. If this point is actually stable (does not change position in time) and it happens to be on the physical axis (axle) then you have a smooth mechanical motion as desired by engineers (and car owners).
This does not mean in any way that the motion can be decsribed only as rotation about this special point. If you mark a point with paint on the carnckshaft, at any time there is rotation of the other points about this paint dot. By this I mean that the velocity of any point relative to the paint dot can be written as $\vec{v_i}=\vec{\omega}\times \vec{r_i}$ were $\vec{r_i}$ is the position of the point i relative to the dot and $\omega$ is the same for any point i and also the same for any choice of the paint dot.
This is what I mean when I say that there is rotation about any point and this is how the motion is described in mechanics books. So, if you say that there is no rotation about points not on the physical axis, you should explain what do you mean by this. It should be a different definition, maybe.