Show that at placing a cork in such a fluid, this will rotate on a plane parallel to the plane $z = 0$, in a...
Assume that $F(x, y, z) = (-y, x, 0)$ represents the velocity field of a fluid in $mathbb{R}^3$. Show that at placing a cork in such a fluid, this will rotate on a plane parallel to the plane $z = 0$, in a circular path around the $z$ axis and also the cork will turn on its own axis.
Here let F be velocity vector field of fluid on $R^3$ defined by F(x,y,z)=-yi+xj. is something interesting that I found about this problem, but they do not solve the whole problem and I think the answer is inconclusive.
I would like to know what I should do here, do I have to calculate the rotational of this field? How do I interpret the result? Thanks
calculus integration multivariable-calculus vector-fields
asked Nov 18 at 16:20
user425181
425310
add a comment |
Assume that $F(x, y, z) = (-y, x, 0)$ represents the velocity field of a fluid in $mathbb{R}^3$. Show that at placing a cork in such a fluid, this will rotate on a plane parallel to the plane $z = 0$, in a circular path around the $z$ axis and also the cork will turn on its own axis.
Here let F be velocity vector field of fluid on $R^3$ defined by F(x,y,z)=-yi+xj. is something interesting that I found about this problem, but they do not solve the whole problem and I think the answer is inconclusive.
I would like to know what I should do here, do I have to calculate the rotational of this field? How do I interpret the result? Thanks
calculus integration multivariable-calculus vector-fields
asked Nov 18 at 16:20
user425181
425310
add a comment |
Assume that $F(x, y, z) = (-y, x, 0)$ represents the velocity field of a fluid in $mathbb{R}^3$. Show that at placing a cork in such a fluid, this will rotate on a plane parallel to the plane $z = 0$, in a circular path around the $z$ axis and also the cork will turn on its own axis.
Here let F be velocity vector field of fluid on $R^3$ defined by F(x,y,z)=-yi+xj. is something interesting that I found about this problem, but they do not solve the whole problem and I think the answer is inconclusive.
I would like to know what I should do here, do I have to calculate the rotational of this field? How do I interpret the result? Thanks
calculus integration multivariable-calculus vector-fields
asked Nov 18 at 16:20
user425181
425310
Assume that $F(x, y, z) = (-y, x, 0)$ represents the velocity field of a fluid in $mathbb{R}^3$. Show that at placing a cork in such a fluid, this will rotate on a plane parallel to the plane $z = 0$, in a circular path around the $z$ axis and also the cork will turn on its own axis.
Here let F be velocity vector field of fluid on $R^3$ defined by F(x,y,z)=-yi+xj. is something interesting that I found about this problem, but they do not solve the whole problem and I think the answer is inconclusive.
I would like to know what I should do here, do I have to calculate the rotational of this field? How do I interpret the result? Thanks
calculus integration multivariable-calculus vector-fields
calculus integration multivariable-calculus vector-fields
asked Nov 18 at 16:20
user425181
425310
asked Nov 18 at 16:20
user425181
425310
asked Nov 18 at 16:20
user425181
425310
asked Nov 18 at 16:20
user425181
425310
asked Nov 18 at 16:20
user425181
425310
425310
add a comment |
add a comment |
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