# Question about axis of rotation and center of gravity

## Recommended Posts

Now, if I am not mistaken, from what I know, the axis of rotation of a body usually goes through the center of gravity of a body. Also, the position of the center of gravity, if I recall correctly, does change when the position of the body of the living being or object in question changes. Well, just to make sure, I must ask: would the location of the axis of rotation change if the position of the center of gravity changes as well?

##### Share on other sites
34 minutes ago, SilentSky23 said:

Now, if I am not mistaken, from what I know, the axis of rotation of a body usually goes through the center of gravity of a body

Yes you are seriously mistaken.

Just think of a solid heavy weight swung round on a long string.

The centre of rotation is the hand holding the other end of the string

The centre of mass is somewhere inside the heavy weight.

Just to be precise, "the centre of gravity is on the line through a body leading to the centre of the Earth, that the weight of that body appears to act."

And the axis of rotation is determined mostly by external agencies.

40 minutes ago, SilentSky23 said:

Also, the position of the center of gravity, if I recall correctly, does change when the position of the body of the living being or object in question changes

Might be better to phrase this

The centre of gravity or centre of mass of a body may change if the configuration of the parts of the body changes.

44 minutes ago, SilentSky23 said:

Well, just to make sure, I must ask: would the location of the axis of rotation change if the position of the center of gravity changes as well?

And the axis of rotation is determined mostly by external agencies.

##### Share on other sites

Studiot is absolutely right AFAICT now, and has given a very thorough discussion AFAICT.

Maybe you mean the 'principal axes.' But even in that case I don't think it's necessarily true, although I would have to think about it. What is true is the (mathematical) fact that, when you refer the motion to the centre of mass, the eqs. of motion adopt a particularly simple way in terms of the moments of inertia relative to the principal axes. They kind of split in to translation and rotation in a simple way.

1 minute ago, joigus said:

Studiot is absolutely right AFAICT now, and has given a very thorough discussion AFAICT.

Maybe you mean the 'principal axes.' But even in that case I don't think it's necessarily true, although I would have to think about it. What is true is the (mathematical) fact that, when you refer the motion to the centre of mass, the eqs. of motion adopt a particularly simple way in terms of the moments of inertia relative to the principal axes. They kind of split in to translation and rotation in a simple way.

Maybe it's true. But then again, I would have to think about it.

Edited by joigus

##### Share on other sites

Here are two very easy examples.

1. Go to the door of the room you are in
Take the handle.
Open and close the Door.
The door rotates about a (hopefully vertical) axis through the hinges.
You are the external agent and apply a force at the handle.
But where is the centre of gravity of the door?
Somewhere in the middle of the door.
2. Take a sheet of paper and a drawing pin.
Pin the paper loosely to a pinboard by the top left corner so the paper swing round under its own weight.
Now change the pin to the bottom right corner.
Once again centre of gravity is in the meiddle of the paper, but
The axis of rotation (the pin) is somewhere else and is now horizontal.

##### Share on other sites

I only said the through the center of gravity part because I kept reading that online and in books. At least for the human body int he pelvic area. Maybe I phrased it wrong, and meant intersect at the center of gravity? If that means anything? Or is the line through the center of gravity?

Edited by SilentSky23

##### Share on other sites
47 minutes ago, studiot said:

Yes you are seriously mistaken.

Just think of a solid heavy weight swung round on a long string.

The centre of rotation is the hand holding the other end of the string

I'm not sure I would call that "rotation". But perhaps the OP (and me) is thinking of something with no external forces applied. In which case, they would be correct, no?

##### Share on other sites
Just now, Strange said:

I'm not sure I would call that "rotation". But perhaps the OP (and me) is thinking of something with no external forces applied. In which case, they would be correct, no?

Yeah, I wasn't really talking about external forces here.

##### Share on other sites

Studiot is correct in the case where an external force is actively causing rotation.

Maybe you mean the case where an initial force causes rotation of a system of 'loose' objects, and then through collapse, and angular momentum conservation, picks up rotational speed.
it would tend to rotation about the axis passing through its center of mass ( which might not necessarily be its center of gravity ).

X-posted with Strange and SilentSky23

##### Share on other sites
2 minutes ago, MigL said:

Studiot is correct in the case where an external force is actively causing rotation.

Maybe you mean the case where an initial force causes rotation of a system of 'loose' objects, and then through collapse, and angular momentum conservation, picks up rotational speed.
it would tend to rotation about the axis passing through its center of mass ( which might not necessarily be its center of gravity ).

X-posted with Strange and SilentSky23

Isn't the external force just the cause of rotation, though? Rather than the line acting through a point in the body? I thought those were two different things. The line part was what I meant by axis of rotation.

##### Share on other sites
11 minutes ago, SilentSky23 said:

Isn't the external force just the cause of rotation, though?

Right; the external force does not need to act through any axis.
A 'torque' can be offset from the center of mass, and impart rotation.

A top can spin about the axis through its center of mass, but it might be at an angle to the vertical, so it isn't spinning through its center of gravity.
( rotations that don't pass through the CoM, lead to imbalances, and that 'torque' will tend realign the rotation, or in extreme cases, break apart the rotating object  ). So make sure your wheels/tires are properly balanced.

This is one of those questions where framing the question correctly gives you one right answer, but not being specific enough gives you many possible right answers

Edited by MigL

##### Share on other sites
2 minutes ago, MigL said:

Right; the external force does not need to act through any axis.
A 'torque' can be offset from the center of mass, and impart rotation.

A top can spin about the axis through its center of mass, but it might be at an angle to the vertical, so it isn't spinning through its center of gravity.
( rotations that don't pass through the CoM, lead to imbalances, and that 'torque' will tend realign the rotation, or in extreme cases, break apart the rotating object  ). So make sure your wheels/tires are properly balanced.

This is one of those questions where framing the question correctly gives you one right answer, but not being specific enough gives you many possible right answers

My bad, I should have known that not all rotations act through the center of mass, something I learned by looking up before you made this post. I should have thought this more carefully before I made this topic. Maybe I was not talking about axis of rotation, but maybe moment of inertia? If moment of inertia has anything to do with center of gravity, does moment of inertia change when the center of gravity changes?

Either way, I am interested in the part of your post I bolded. Can you please tell me more, if you can?

##### Share on other sites

It's common to take the moment of inertia of a body about an axis running through the center of gravity. It represents the inertial resistance to accelerating the body rotationally about that particular axis, and can depend on the choice of axis.

I'm not sure that is what you are after though.

##### Share on other sites
49 minutes ago, SilentSky23 said:

My bad, I should have known that not all rotations act through the center of mass, something I learned by looking up before you made this post. I should have thought this more carefully before I made this topic. Maybe I was not talking about axis of rotation, but maybe moment of inertia? If moment of inertia has anything to do with center of gravity, does moment of inertia change when the center of gravity changes?

Either way, I am interested in the part of your post I bolded. Can you please tell me more, if you can?

Centre of mass, moments of inertia (there are 6 of them for a rigid body) and any other average of any power of the coordinates with respect to the mass distribution will change if or when you change the mass distribution. If you think about it, it will make sense, I believe.

Rotating a body around an axis that is not a principal axis will lead to mechanical stress that could result in breaking it. In general, having a rigid body rotate around any axis that is not an axis of "inertial symmetry" will lead to such mechanical stresses and tend to break it, if it's rigid. One simple way to do that is by forcing one such body to rotate around any axis that is not a principal axis of rotation (the axis the masses cluster around as symmetrically as possible, so to speak.)

Whether the balance of forces would realign the rotation depends on the detailed study of the solutions to the problem. It would be very surprising to me that the situation you are proposing lead to a point of stable equilibrium in the phase space (the space of all dynamical configurations.) Stability and predictability are exceptions, not the norm.

On the contrary, if you do the same with a blubbery gooey kind of object, the rotation would lead to deformations, although the moment of inertia as such would not be well defined. Or you could perhaps work out some kind of instantaneous moment of inertia definition.

I hope the previous was helpful. If not, just ignore me.

1 hour ago, MigL said:

A top can spin about the axis through its center of mass, but it might be at an angle to the vertical, so it isn't spinning through its center of gravity.
( rotations that don't pass through the CoM, lead to imbalances, and that 'torque' will tend realign the rotation, or in extreme cases, break apart the rotating object  ). So make sure your wheels/tires are properly balanced.

Yeah, probably MigL is right that it could realign the rotation. I'm just not sure right now. I think that had to do with the combined action of gravity and friction.

1 hour ago, MigL said:

This is one of those questions where framing the question correctly gives you one right answer, but not being specific enough gives you many possible right answers

Ditto.

11 minutes ago, J.C.MacSwell said:

I'm not sure that is what you are after though.

Ditto.

9 minutes ago, joigus said:

In general, having a rigid body rotate around any axis that is not an axis of "inertial symmetry" will lead to such mechanical stresses and tend to break it, if it's rigid.

For big angular velocities, not necessarily accelerations, as rotations always induce non-inertial forces.

Edited by joigus
corrected symmetry argument tensor of inertia

##### Share on other sites

There are three possible sets of axes connected with rotations.
Each of these sets can be variously oriented with respect to the others, and also offset by a distance.

1) We have the general axes in which you are working, say two horizontal, and a vertical one. Or up/ down ; forward/back ; left/right.

2) Then we have what joigus was talking about which are called the axes of inertia.
The principal axes of inertia are obtained when the 'cross products of inertia' are zero and you are left only with moments of inertia and the radius of gyration.

3) The so called Euler axes which are an orthogonal set (mutually perpendicular) about which we apply three separate torques. They are probably what MigL was talking about.

I have posted this experiment before.

Take a brick shaped object such as a brick, book, matchbox empty chocolate box etc.
Imagine an axis of rotation through each of the three pairs of opposite faces. So they correspond to pitch, roll and yaw in aviation or boating parlance.
In turn, toss the object into the air giving it a spin about one of the axes.

You will find that the spin is stable abot two axes and unstable about the third.

Edited by studiot

##### Share on other sites
2 hours ago, joigus said:

Whether the balance of forces would realign the rotation depends on the detailed study of the solutions to the problem.

Yeah, I was thinking along the lines of this ancient centrifugal separator we use at work.
A slurry is pumped into a large, filtering drum which is rotating rapidly.
The cloth filter traps solid particles ( mostly sulfur with some triisobutyldithiophosphinate ), and although pumped in asymmetrically, the slurry/solids disperse around the perimeter and effectively become filtering media.

If this didn't happen, the imbalance would ruin the bearings in a matter of minutes.

##### Share on other sites
3 hours ago, J.C.MacSwell said:

It's common to take the moment of inertia of a body about an axis running through the center of gravity. It represents the inertial resistance to accelerating the body rotationally about that particular axis, and can depend on the choice of axis.

I'm not sure that is what you are after though.

What I was after was if anything rotation based in physics, like moment of inertia and such, is connected to center of gravity, to the point that anything rotation based changes when the center of mass changes. Like if the center of gravity is outside the body, mainly a non-rigid body, does anything like moment of inertia change as in become easier or harder.

Why would it be hard to understand?

##### Share on other sites
6 hours ago, SilentSky23 said:

Now, if I am not mistaken, from what I know, the axis of rotation of a body usually goes through the center of gravity of a body. Also, the position of the center of gravity, if I recall correctly, does change when the position of the body of the living being or object in question changes. Well, just to make sure, I must ask: would the location of the axis of rotation change if the position of the center of gravity changes as well?

I have been trying to play down the mathematics since I know you are not big on that.

But once you are talking about rotation and  deformable bodies you are into the mechanics of materials ie shear stress, which is a rotation.
Such rotations are not connected with the COG of the body.

Further rotational mechanics arises in the dynamics of fluids, again the centre of gravity does not play a large part in this.

So some examples from you of the situations you wish to examine would be useful.

You continue to use the term centre of gravity and I tried to explain the difference between the centres of mass and gravity.

I hope you understood it. COGs are only important in a gravitational field, and particularly when gravity is the main force acting.

##### Share on other sites
2 minutes ago, studiot said:

I have been trying to play down the mathematics since I know you are not big on that.

But once you are talking about rotation and  deformable bodies you are into the mechanics of materials ie shear stress, which is a rotation.
Such rotations are not connected with the COG of the body.

Further rotational mechanics arises in the dynamics of fluids, again the centre of gravity does not play a large part in this.

So some examples from you of the situations you wish to examine would be useful.

You continue to use the term centre of gravity and I tried to explain the difference between the centres of mass and gravity.

I hope you understood it. COGs are only important in a gravitational field, and particularly when gravity is the main force acting.

Sorry. I forgot to use center of gravity, and I did not understand how complex this was.

For examples, what about a gymnast doing, well,  a back flip or another gymnastics routine if that counts? That was mainly what I was going for, anyway.

Also, forget center of gravity. Let's use center of mass for the question I was asking, instead.

##### Share on other sites
8 minutes ago, SilentSky23 said:

Sorry. I forgot to use center of gravity, and I did not understand how complex this was.

For examples, what about a gymnast doing, well,  a back flip or another gymnastics routine if that counts? That was mainly what I was going for, anyway.

Also, forget center of gravity. Let's use center of mass for the question I was asking, instead.

Gravity plays a huge part in the activity of gymnasts, skaters, swimmers and many other athletes.
One of the most important issues is the effect of centre of gravity on balance.

Is this the sort of thing you want to talk about?

##### Share on other sites
1 minute ago, studiot said:

Gravity plays a huge part in the activity of gymnasts, skaters, swimmers and many other athletes.
One of the most important issues is the effect of centre of gravity on balance.

Is this the sort of thing you want to talk about?

That should do, and if it didn’t, close enough. Thanks.

##### Share on other sites

So can you articulate a complete question now?

One further question.
Are you familiar with the idea of stable unstable and metastable equilibrium ?

##### Share on other sites
1 minute ago, studiot said:

So can you articulate a complete question now?

One further question.
Are you familiar with the idea of stable unstable and metastable equilibrium ?

I will try next time.

And no.

##### Share on other sites
6 minutes ago, SilentSky23 said:

I will try next time.

And no.

A system or body is said to be in stable, unstable or metastable equilibrium, depending upon what happens if a small chage or displacement is made/given to it.

So consider the ball in my picture.

1) At the top of the hill it is in unstable equilibrium because a small push either way will cause it to roll down the hill ( a big change)

2) On the level bench it is in metastable equilibrium because if pushed one way (uphill) it will roll back, but if pushed the other it will eventually roll down to the bottom.

3) At the bottim if pushed either way it will roll back to the bottom.

Acrobatic rotations are like this. They can either carry you over or flip you back or balance you against falling.

In boats there is a thing called the metacentre, the position of which relative to the centre of gravity, indicated whether the boat will self right if it rolls over.

##### Share on other sites
1 hour ago, MigL said:

Yeah, I was thinking along the lines of this ancient centrifugal separator we use at work.
A slurry is pumped into a large, filtering drum which is rotating rapidly.
The cloth filter traps solid particles ( mostly sulfur with some triisobutyldithiophosphinate ), and although pumped in asymmetrically, the slurry/solids disperse around the perimeter and effectively become filtering media.

If this didn't happen, the imbalance would ruin the bearings in a matter of minutes.

Yeah, I was pigeonholed in my theoretical mind. Couldn't think about fluids and the like. The OP I think was talking about sth. like biomechanics.

1 hour ago, SilentSky23 said:

What I was after was if anything rotation based in physics, like moment of inertia and such, is connected to center of gravity, to the point that anything rotation based changes when the center of mass changes. Like if the center of gravity is outside the body, mainly a non-rigid body, does anything like moment of inertia change as in become easier or harder.

Why would it be hard to understand?

Sorry on my part: Yes! Everything rotation-based in physics changes when you displace the centre of mass, or the centre of gravity if you rotate about the same axis.

The best example I can think of is a pole dancer. These girls must really get some joint lesions from the stress of rotating out of centre.

Edited by joigus

##### Share on other sites
49 minutes ago, studiot said:

I have been trying to play down the mathematics since I know you are not big on that.

But once you are talking about rotation and  deformable bodies you are into the mechanics of materials ie shear stress, which is a rotation.
Such rotations are not connected with the COG of the body.

Further rotational mechanics arises in the dynamics of fluids, again the centre of gravity does not play a large part in this.

So some examples from you of the situations you wish to examine would be useful.

You continue to use the term centre of gravity and I tried to explain the difference between the centres of mass and gravity.

I hope you understood it. COGs are only important in a gravitational field, and particularly when gravity is the main force acting.

Hi Studiot

I understand what you are saying (makes sense) but for most purposes there is very very little difference...to the point that they are commonly interchangeable. The gravitational gradients we generally deal with are pretty small relative to the objects we normally consider in mechanics, and any reorientation of the object does insignificantly little to change any difference...they pretty much move together.

When someone says COG they usually mean COM.

## Create an account

Register a new account