Why do rotating bodies continue to spin without an external torque?

[pinsky]

I have spent some time puzzleing myself about rotation. If we examine Newtons laws for linear motion, they say that the body stands still or continues to move at the same velocity if no force acts upon it.

Now if i try to convert that theorem for rotation of rigid bodies, i get a bit confused. If we have a rotating body in idealised conditions (vacume and no gravity) on which a force (or torque) isn't acting, what keeps it spining? (considering that there is no rotation without centripetal acceleration.


I have a assumption for an answer, but ain't sure if its correct.

(i'm observing the body as two spheres atachet to a weightless stick, kind of those things majoretes whirl on parades)

My assumption is that if the body axes of rotation is also its simetry axes, than the simetrical masses on opposite sides provide the centripetal acceleration for each other and that's why the body can spin without an external torque.


Another problem i have is when observing rotating bodies around axis different than the simetry axel. My assumtion is that in thouse cases, we are only changing the system from which we are observing the body, but in the end if there is no external force that results the continuous rotation (at the same velocity), it is a ok to assume that the body is rotation around it's simetry axes.


Example:

If we have a board on frictionless ice which is standing still, on whose end a man jumps (none of them is weightless), the board (with the man on it) will start to rotate around the newly formed center of mass, irelevant of which axis we choused as the rotation axis for our calculation.

The system will also have a translational movement, but for a rightly chosen axes of rotation (areoun the newla formed centar of mass) the translation movement won't nahe any influence on the rotation equations.


Comments?

 

[tiny-tim]

hi pinsky!

If we examine Newtons laws for linear motion, they say that the body stands still or continues to move at the same velocity if no force acts upon it.

Now if i try to convert that theorem for rotation of rigid bodies …

the rotational version of that law is that the body stands still or continues to rotate at the same angular velocity if no https://www.physicsforums.com/library.php?do=view_item&itemid=175" acts upon it

Another problem i have is when observing rotating bodies around axis different than the simetry axel. My assumtion is that in thouse cases, we are only changing the system from which we are observing the body, but in the end if there is no external force that results the continuous rotation (at the same velocity), it is a ok to assume that the body is rotation around it's simetry axes.

the https://www.physicsforums.com/library.php?do=view_item&itemid=313"(which is what you need) can be calculated about any axis …

the angular momentum about any axis is the sum of the angular momentum about a parallel axis through the centre of mass plus the angular momentum of the same total mass moving with the position and velocity of the centre of mass

(and the angular velocity, ω, is the same no matter which axis you choose)

 

[D H]

the rotational version of that law is that the body stands still or continues to rotate at the same angular velocity if no https://www.physicsforums.com/library.php?do=view_item&itemid=175" acts upon it

That is only true in the special case of an object rotating about an eigenaxis. While angular momentum is a conserved quantity, angular velocity in general is not.

 

[tiny-tim]

oooh, yes, that's right …

i was a bit too keen on copy-and-pasting …

i should have changed it to "… the body stands still or continues to rotate with the same angular momentum if no torque acts upon it" …

thanks D H ​