- #1
freemind
One simple question: why do liquid mirrors assume a parabolic shape when subject to uniform angular motion? (I mean, why not circular, or some other reasonably curved shape?)
Last edited by a moderator:
Why Do Spinning Liquid Mirrors Assume a Parabolic Shape?
In summary, liquid mirrors assume a parabolic shape when subject to uniform angular motion because of the forces of gravity and centrifugal force. The definition of a parabola, with equidistant points from a point and a plane, explains the shape. Centrifugal force increases with distance, while gravity remains constant. This results in a curved shape rather than a circular one.
- #2
Chronos
Science Advisor
Gold Member
- 11,440
- 750
Think in terms of the definition of a parabola - the path followed by a plot of points equidistant from a point and a plane. You have two forces in play with a spinning liquid, gravity and centrifugal force. Centrifugal force pushes the liquid along the x - axis, gravity attracts the liquid along the y - axis. The centrifugal force component increases with the square of the distance from the center whereas the gravitational force component remains constant.
- #3
freemind
Wow, that makes so much sense! Thanks a lot Chronos. 
1. What is the shape of spinning liquid?
The shape of spinning liquid is typically a paraboloid, which is a three-dimensional curved shape similar to a bowl or a satellite dish. This shape is caused by the centrifugal force of the spinning motion, which pulls the liquid towards the edges and creates a concave surface in the middle.
2. How does the speed of spinning affect the shape of liquid?
The faster the liquid is spun, the more pronounced the paraboloid shape becomes. This is because the centrifugal force is stronger at higher speeds, pulling the liquid towards the edges even more.
3. Can the shape of spinning liquid be controlled?
Yes, the shape of spinning liquid can be controlled by changing the speed and direction of the spinning. The shape can also be influenced by the size and shape of the container holding the liquid.
4. What factors can affect the stability of the shape of spinning liquid?
The stability of the shape of spinning liquid can be affected by various factors, such as the viscosity and surface tension of the liquid, as well as the speed and direction of the spinning. Other factors may include external forces or disturbances, such as vibrations or uneven surfaces.
5. How is the shape of spinning liquid used in scientific research?
The shape of spinning liquid is used in various scientific studies, such as fluid dynamics, astrophysics, and material science. It can also be used as a model for understanding the behavior of other spinning objects, such as planets and galaxies. Additionally, the shape of spinning liquid has practical applications, such as in centrifuges for separating mixtures and in gyroscopes for navigation.
Similar threads
-
Classical Physics
-
Classical Physics
-
Classical Physics
-
Thermodynamics
-
Classical Physics
-
Astronomy and Astrophysics
-
DIY Projects
-
Classical Physics