Why do objects always rotate about their centre of mass?

[hutchphd]

Boat moves in circle around point A, but boat do not rotate(change orientation) because allways same side of boat looking toward point A.

Boat dont spins around itself.

This is simply incorrect.
If you don't see it then you don't see it.
For the boat not to rotate, the prow would need to point at a fixed point very far away....say Bangor Maine. Does your boat always point at Bangor?

 

[vanhees71]

This is simply incorrect.
If you don't see it then you don't see it.
For the boat not to rotate, the prow would need to point at a fixed point very far away....say Bangor Maine. Does your boat always point at Bangor?

But it's easy to see. Just put your body-fixed coordinate system (body-fixed origin and Cartesian body-fixed basis) and draw it for different times. You'll see that the body-fixed basis rotates relative to the space-fixed (inertial) basis. Only the decomposition of the motion in translatiional parts (i.e., the motion of the body-fixed origin relative to the space-fixed origin) and rotational parts (i.e., the motion of the other points of the body relative to the body-fixed origin) changes by changing the body-fixed origin. The overall motion is of course the same irrespective of the choice of any reference frames.

 

[A.T.]

Boat moves in circle around point A, but boat do not rotate(change orientation)

In the rest frame of the water, which you claimed to use, the boat does change orientation.

because allways same side of boat looking toward point A.

In the rest frame of the water, the vector (boat -> A) changes orientation as well.

 

[John Mcrain]

In the rest frame of the water, which you claimed to use, the boat does change orientation.In the rest frame of the water, the vector (boat -> A) changes orientation as well.

Yes it will not change orientation(rotate) if bow point allways to the north.

 

[A.T.]

Yes it will not change orientation(rotate) if bow point allways to the north.

Right, but is not likely to be case here, so the boat is rotating. Around which point is a matter of choice.

 

[John Mcrain]

Right, but is not likely to be case here, so the boat is rotating. Around which point is a matter of choice.

I agree. one rotation per one full circle.

Is point about boat travel in circular path also metter of choise or it only can be point A?

 

[hutchphd]

Sticking with boats: Suppose two identical boats are tied with a rope at the gunnels (pointing opposite directions). Each boat will travel in a circle about the centerpoint of the rope (point A). But each boat captain will correctly rerport also that the other boat is circling about his boat. And that his own boat is rotating about its center!
They are all correct descriptions.....So not really specific enough. Can we be finished now?

 

[A.T.]

Is point about boat travel in circular path also metter of choise or it only can be point A?

If you want a center of the circular translation that is static in the rest frame of the water, then it can only be A.

 

[John Mcrain]

If you want a center of the circular translation that is static in the rest frame of the water, then it can only be A.

Finally came to mine

 

[Dale]

Finally came to mine

Notice he said center of circular translation, not center of rotation.

 

[John Mcrain]

Notice he said center of circular translation, not center of rotation.

It will be easier to learn with examples of solving tasks or animations, not with words.
For example after I watched this animation I figure out why my boat and moon rotate as well.

 

[hutchphd]

It will be easier to learn with examples of solving tasks or animations, not with words.

It will be easier for you. The statement is otherwise presumptuous.
For many technical trained people, the math is by far the easiest. Vectors make the entire world far more comprehensible.

 

[russ_watters]

Finally came to mine

You may not be aware, but you've created a potential contradiction for yourself here by having two different axes. One for the rotation and a different one for the translation.

 

[A.T.]

It will be easier to learn with examples of solving tasks or animations, not with words.
For example after I watched this animation I figure out why my boat and moon rotate as well.

Note that by limiting yourself to a special case where rotation and circular translation have the same frequency you are setting yourself up to confuse them. You should look at other cases to understand the difference between them and their possible centers.