A few questions about angular momentum...

[MDJH]

Ok, so first off, angular momentum doesn't need to involve rotational motion, and a particle can have "angular momentum" with respect to an axis if it is moving in a straight line that doesn't pass through the axis, right? Also, if the particle had a constant speed and constant mass, then moving along the axis, its angle with respect to the axis would be perpendicular when the distance TO the radius is the lowest... does this imply that the angular momentum of such a particle would be constant?

 

Also, as for the angular momentum of something thrown into the air... let's say we had a water bottle that was filled part way. It was thrown into the air such that its plane of rotation was parallel to the long end of the bottle. While the bottle would be rotating, the water itself would be moving from one side to the other, and flowing along the edge on the way. Would the moment of inertia in such a case be constant or changing, and as such, would the angular velocity (assuming angular momentum is constant; neglecting influence of air friction) itself be a function of time while the bottle is in the air?

 

And another thing, presumably air friction would act to slow down a rotating object, since air molecules are constantly in random motion and the number of collisions with air molecular will be higher in the direction of motion than away from it, right? And if an object were rotating AND translating, would friction stop both rotation and translation at the same time, or could it stop one before stopping the other?

Edited August 15, 2010 by MDJH

[Mr Skeptic]

Ok, so first off, angular momentum doesn't need to involve rotational motion, and a particle can have "angular momentum" with respect to an axis if it is moving in a straight line that doesn't pass through the axis, right? Also, if the particle had a constant speed and constant mass, then moving along the axis, its angle with respect to the axis would be perpendicular when the distance TO the radius is the lowest... does this imply that the angular momentum of such a particle would be constant?

 

Yes, and also angular momentum is conserved just like energy and regular momentum.

 

Also, as for the angular momentum of something thrown into the air... let's say we had a water bottle that was filled part way. It was thrown into the air such that its plane of rotation was parallel to the long end of the bottle. While the bottle would be rotating, the water itself would be moving from one side to the other, and flowing along the edge on the way. Would the moment of inertia in such a case be constant or changing, and as such, would the angular velocity (assuming angular momentum is constant; neglecting influence of air friction) itself be a function of time while the bottle is in the air?

 

Yup, the moment of inertia can change but angular momentum will be conserved and this will change the rotational velocity.

 

And another thing, presumably air friction would act to slow down a rotating object, since air molecules are constantly in random motion and the number of collisions with air molecular will be higher in the direction of motion than away from it, right? And if an object were rotating AND translating, would friction stop both rotation and translation at the same time, or could it stop one before stopping the other?

 

Yup, friction and drag will slow down both motions simultaneously. However it could be by different amounts, which would largely depend on the properties of the object.

[MDJH]

Yup, friction and drag will slow down both motions simultaneously. However it could be by different amounts, which would largely depend on the properties of the object.

But would both motions tend to come to a stop at the same time, or at different times?

[swansont]

But would both motions tend to come to a stop at the same time, or at different times?

 

You can't make a general statement about that, unless the rotation and translation are coupled. Otherwise it will depend on the details of the system.