| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
22 Mar 2007 09:46:14 PM |
| Object: |
angular acceleration |
I was just wondering if it's always okay to add angular acceleration
to angular velocity (assuming the time is one). I know it's okay in
the two dimensional case, but I just want to be sure about the three
dimensional case.
For instance, you might have an angular acceleration about the x axis
of 2:
a = (2, 0, 0)
Then, you might have an angular acceleration about the y axis of 1.
a = (0, 1, 0)
Then, you might have an angular acceleration about the z axis of 3.
a = (0, 0, 3)
So, the total would be:
w = (2, 1, 3).
Then, I would just add any future angular accelerations to this
vector.
Is it always okay to do this?
Thanks.
.
|
|
| User: "Androcles" |
|
| Title: Re: angular acceleration |
23 Mar 2007 01:45:43 AM |
|
|
<bob@coolgroups.com> wrote in message =
news:1174617974.785407.326770@e1g2000hsg.googlegroups.com...
I was just wondering if it's always okay to add angular acceleration
to angular velocity (assuming the time is one). I know it's okay in
the two dimensional case, but I just want to be sure about the three
dimensional case.
=20
For instance, you might have an angular acceleration about the x axis
of 2:
=20
a =3D (2, 0, 0)
=20
Then, you might have an angular acceleration about the y axis of 1.
=20
a =3D (0, 1, 0)
=20
Then, you might have an angular acceleration about the z axis of 3.
=20
a =3D (0, 0, 3)
=20
So, the total would be:
=20
w =3D (2, 1, 3).
=20
Then, I would just add any future angular accelerations to this
vector.
=20
Is it always okay to do this?
=20
Thanks.
No.
If you rotate in the x-y plane about the origin
then you move in both x and y.
If you rotate in the y-z plane about the origin
then you move in both y and z.
If you then rotate in the x-z plane about the origin
then you move in both x and z, but you've already
done that.
Example:=20
The point (1,0,0) is rotated to (0,1,0) in the x-y plane.
It is then rotated in y-z plane to (0,0,1).
This is identical to a rotation in the x-z plane from=20
(1,0,0) to (0,0,1).
There is no combination of rotations=20
(1,0,0)
(0,1,0)
(0,0,1)
that will take you from (0,0,0) to (1,1,1) simply
by adding.
That is moving linearly from the centre of a sphere
to its surface, not a rotation.=20
.
|
|
|
| User: "Autymn D. C." |
|
| Title: Re: angular acceleration |
23 Mar 2007 04:04:41 AM |
|
|
Androcles flunks the word/maths/reck problem anoth.
.
|
|
|
|
|
| User: "Sam Wormley" |
|
| Title: Re: angular acceleration |
22 Mar 2007 10:32:47 PM |
|
|
wrote:
I was just wondering if it's always okay to add angular acceleration
to angular velocity (assuming the time is one).
That would make about as much sense as adding acceleration to
velocity! One is the derivative of the other with respect to
time.
.
|
|
|
|
| User: "Edward Green" |
|
| Title: Re: angular acceleration |
01 Apr 2007 07:21:38 PM |
|
|
On Mar 22, 10:46 pm, wrote:
I was just wondering if it's always okay to add angular acceleration
to angular velocity (assuming the time is one). I know it's okay in
the two dimensional case, but I just want to be sure about the three
dimensional case.
For instance, you might have an angular acceleration about the x axis
of 2:
a = (2, 0, 0)
Then, you might have an angular acceleration about the y axis of 1.
a = (0, 1, 0)
Then, you might have an angular acceleration about the z axis of 3.
a = (0, 0, 3)
So, the total would be:
w = (2, 1, 3).
Then, I would just add any future angular accelerations to this
vector.
Is it always okay to do this?
As Sam Wormley points out, you seem to have some confusion regarding
derivatives. What you propose _might_ make sense if you mean "the
effect of a given angular acceleration acting over 1 second".
Probably you should just ask if angular acceleration adds at a
particular instant.
Rotational dynamics are confusing enough for a lifetime. Not
everything which looks like it might be a vector acts like a vector.
A finite rotation about a given axis looks like it might be a vector
(we specify a direction in space and, taking a positive sense by the
right hand rule, a magnitude of rotation: direction + magnitude =>
vector?), yet finite rotations do not add like vectors: in
particular, they do not commute.
Angular velocity looks like a vector (the magnitude and direction
thing again), and yet its components do not behave like we expect
vector components to behave: the formal z-component of angular
velocity does not correspond to a projected rate of rotation about the
z-axis the way that the z-component of (linear) velocity correponds to
the projected velocity on the z-axis.
Angular momentum does behave like a bonafide vector (except under
coordinate reflections), and I suspect angular velocity does too,
despite the problem with interpreting its components. Or does it?
It's related to angular momentum by the moment of inertia tensor --
that's encouraging -- but does it make sense to "add" two angular
velocities? And how can this "velocity" be both a vector, and
(apparently), the derivative of something which is not a vector
(angular displacement)? Or is it wrong to assume angular "velocity"
can be interpreted as the derivative of angular "displacement"?
Happy to help clear up your confusion. :-)
.
|
|
|
|
|
Related Articles |
|
|
