What is the relationship between rotating objects and their surfaces?

[fisico30]

but when the rake is flying in the air the center of mass has no support under it to balance it.
Sure, the weight force acts on the center of mass.

Do we assume that the object, if it rotates, must always rotate about the center of mass? In that case weight exerts zero torque...

thanks
fisico30

 

[tiny-tim]

Do we assume that the object, if it rotates, must always rotate about the center of mass? In that case weight exerts zero torque...

no, it doesn't rotate about the centre of mass …

it can only do that if the centre of mass is (instantaneously) stationary!​

yes, gravity exerts zero torque, and so it cannot affect the angular velocity … if you flip something into the air, whatever angular velocity it has when you let go, it keeps (while gravity makes the centre of mass move along a parabola)

 

[fisico30]

Thank you again.

So, about what point does the object flying in the air rotates about?
If we were on the object, on which point would we seat and see everything else rotate around us while we translate along the parabolic trajectory?

Tiny-tim, you mention that it can only do that if the centre of mass is (instantaneously) stationary!.

Do you have an example? When would the CM be instantaneously at rest from the lab reference frame?

thanks
fisico30

 

[tiny-tim]

So, about what point does the object flying in the air rotates about?

could be anywhere

eg if it was thrown vertically upward (while rotating), the instantaneously stationary point about which it instantaneously rotates would be somewhere on the horizontal line through the centre of mass

If we were on the object, on which point would we seat and see everything else rotate around us while we translate along the parabolic trajectory?

i'm not sure what you mean

if we were at the centre of mass, we would see the whole object rotate around us, while we follow a parabola

Tiny-tim, you mention that it can only do that if the centre of mass is (instantaneously) stationary!.

Do you have an example? When would the CM be instantaneously at rest from the lab reference frame?

in the lab frame, never, unless the motion is purely vertical, and the object is exactly at the top of its flight

 

[fisico30]

Ok, so you call "instantaneous" the point of rotation (I guess we should talk about the axis of rotation) because it changes with time with respect to the lab frame?

But from the point of view of the flying object, the only point that is not rotating is the CM...
that is why I continue to call that the center of rotation of the unconstrained flying object..

fisico30

 

[tiny-tim]

Ok, so you call "instantaneous" the point of rotation (I guess we should talk about the axis of rotation) because it changes with time with respect to the lab frame?

yes

But from the point of view of the flying object, the only point that is not rotating is the CM...
that is why I continue to call that the center of rotation of the unconstrained flying object..

i see what you mean, and that's certainly a valid way of describing the motion (the centre of mass follows a parabola, and the body rotates about it), but it isn't actually the centre of rotation

 

[fisico30]

Tiny-tim,

when I asked about the orientation of each triad of principal axes associated to each point inside an extended object, you replied that principal axes associated to different points are parallel to each other...How do you know that? Where can I find a proof of it? Goldstein book maybe?

My basic mechanics book don't mention that interesting aspect...

thanks
fisico30

 

[fisico30]

As far as the center of rotation and axis of rotation, if we are at the origin of our frame of reference (relative to which we are at rest), and a car drives by, the car is rotating about our location. In fact the car, even if it is moving in a straight line, has angular momentum
p=mvr sin(theta).

So, what is the axis of rotation? It is a straight line (can it be curved? Maybe so, in deformable objects) formed by points that are at rest relative to other moving points.
In a sense, every point or points that are attached to the frame of reference represent centers of rotation...do they?

thanks
fisico30