An isolated object can rotate only about its center of mass

[jbriggs444]

I meant if I and my friend are holding each other’s hand and are rotating (consider we are in motion already, we didn’t begin from rest) and now if we try rotating each other a little fastly, won’t our angular velocity going to increase?

Please specify exactly how you are going to increase your partner's angular momentum without reducing your own.

Yes, there is a technique that you can use to increase your angular velocity using internal forces -- you pull your partner toward yourself. But there is no technique that allows you to increase your angular momentum using only internal forces.

 

[Adesh]

Please specify exactly how you are going to increase your partner's angular momentum without reducing your own.

Yes, there is a technique that you can use to increase your angular velocity using internal forces. But there is no technique that allows you to increase your angular momentum using only internal forces.

Yes, I have completely understood you. Now, please explain that main question to me.

 

[jbriggs444]

Yes, I have completely understood you. Now, please explain that main question to me.

I do not understand. What do you want explained? What is the "main question" in your mind?

 

[Adesh]

I do not understand. What do you want explained? What is the "main question" in your mind?

How can an isolated body only rotate about its CM? What restricts it to rotate about any other point ?

 

[jbriggs444]

How can an isolated body only rotate about its CM? What restricts it to rotate about any other point ?

That is mostly a question of semantics and not of physics. The relevant physics is covered in post #2.

The semantics: What do you mean when you say that an object rotates about a point? Is that point itself allowed to move over time? In what ways?

 

[Adesh]

The semantics: What do you mean when you say that an object rotates about a point? Is that point itself allowed to move over time? In what ways?

Translational Equilibrium has been established. That is the point about which rotation is caused doesn’t displace with time.

 

[Lnewqban]

@Lnewqban I think rotation involves continuous change of direction (if speed is to be kept constant) i.e. the velocity does change. But you and @jbriggs444 have asserted that no external force is needed for a rotation in isolation. I think I’m missing something.

Going back to your small cube inside that field of parallel lines of force (continuos distribution):
It could be rotating, but that rotation would not be caused by the forces of that imaginary homogeneous field.
Some ancient pair of forces initiated that rotation, way back before the little cube entered our field of equal and parallel forces.
Note that such rotation is not accelerated or decelerated, its angular velocity remains constant respect to time (no new forces are applied).
The direction of that rotation could be in any direction, as it is not affected by the new field of forces.

Think of a floating object in the middle of the stream of a slow river.
The object is not initially rotating respect to the non-turbulent stream.
Then, one side of the object hits a steady rock that is protruding above the surface.
The force of friction with the rock on one side plus the flow of the stream on the opposite side create a pair of forces that induce a rotation.
That rotation would be accelerated only during the time the object and the rock are in contact.
After that moment, the rotation will have a more or less constant angular velocity (with enough time, the actual viscosity friction against the water will slow that rotation until reaching zero angular velocity).

What seems more natural to you: a rotation around an axis that crosses the center of mass of that object or a rotation around an axis tangent to the edge of that object?

 

[Adesh]

What seems more natural to you: a rotation around an axis that crosses the center of mass of that object or a rotation around an axis tangent to the edge of that object?

About center of mass

 

[Adesh]

@Lnewqban Why it seems natural to me?

 

[jbriggs444]

Translational Equilibrium has been established. That is the point about which rotation is caused doesn’t displace with time.

OK. So we have adopted a frame of reference where the center of rotation (if any) is stationary and remains so.

If the center of mass is not at the center of rotation, that means that the center of mass is circling the center of rotation, right? Which means that the center of mass is accelerating, right? And what do we know about the acceleration of the center of mass in the absence of external forces?

Edit: Since you have chosen this particular notion of rotation about a point, I will refrain from trying to introduce the notion of an instantaneous center of rotation for an object whose center of mass is moving.

 

[Lnewqban]

@Lnewqban Why it seems natural to me?

I would say because it is the way it happens in nature in a consistent way.

No matter how you throw a Frisbee disc, a boomerang or a baseball; if they are spinning when leaving your hand, you cannot make them rotate around any axis that is far away from the center of mass.
I would say that the greater the angular momentum, the greater the tendency to spin around the CM would be.

 

[Adesh]

OK. So we have adopted a frame of reference where the center of rotation (if any) is stationary and remains so.

If the center of mass is not at the center of rotation, that means that the center of mass is circling the center of rotation, right? Which means that the center of mass is accelerating, right? And what do we know about the acceleration of the center of mass in the absence of external forces?

Edit: Since you have chosen this particular notion of rotation about a point, I will refrain from trying to introduce the notion of an instantaneous center of rotation for an object whose center of mass is moving.

I got you, thank you so much.

 

[John Mcrain]

How can an isolated body only rotate about its CM? What restricts it to rotate about any other point ?

If CM rotate around some other point that is not CM, that mean you must have external centripetal force to do that.