Centrifugal Force on Rotating Water Container

When a container of water is at rest (in an inertial reference frame) the surface of the water is flat (horizontal). However, when the container of water is placed on a rotating platform and spun at a constant angular velocity, the water height forms the shape of a parabola due to the centrifugal force in the rotating (non-inertial) reference frame.




The observation of this effect was instrumental in encouraging Sir Isaac Newton to develop his laws of motion for inertial reference frames.

This is also the way that large parabolic mirrors are constructed today: molten glass is heated to the melting point in a furnace while the glass is rotating a constant angular velocity.

Category:

Education

Tags:

• Centrifugal Force
• physics
• rotating water
• rotation

[brianburleigh]

No such thing as centriFUGal force. The "force" that is pushing the water toward the corners is actually not a force at all - it's the INERTIA of the water, it's own natural resistance to motion. The water tries to stay still, and the tank is moving, and so it's the tank that forces the water shape like this. A common enough misconception.

[drdanku]

@brianburleigh

Because of the rotation (acceleration) of the reference frame, there are two additional forces that do not exist in an inertial frame: The Coriolis force and the Centrifugal force. These two forces - which are due entirely to the rotation of the reference frame - are absolutely necessary to explain the motion of an object which is moving in a rotating reference frame.

[brianburleigh]

@drdanku I've taken physics beyond the intro level - I have an M.S. in the subject. And I've *had* junior/senior level mechanics, as well as graduate-level mechanics, and the same conclusion remains - there aren't *any* centriFUGal forces. Coriolis forces aren't radially outward and so don't fit the description.

[drdanku]

@brianburleigh

Well, if you've taken a theoretical physics course and used any of the standard textbooks covering the topic (Taylor, Gradstein) then you should have covered this example along with the discussion of Centrifugal forces and Coriolis forces at some point. You cannot explain the parabolic shape of the water (in the reference frame of a rotating platform) without using a Centrifugal force.

[drdanku]

@brianburleigh

Perhaps this is an issue of semantics. When you analyze motion in a rotating reference frame, there is a vector quantity whose direction points outward from the center, and whose magnitude is the product of inertia and acceleration. Such quantities are typically called "forces", and in this case it is called the "centrifugal force." You can argue about "real" versus "fictitious" forces. But, the fact remains there is an outward pointing force-like vector quantity present.

[drdanku]

@drdanku If you are interested in the derivation of the spinning water problem, along with an explanation of why the shape is a parabola, check out "Classical Mechanics: A Modern Perspective" by Vernon D. Barger and Margin G. Olsson, (McGraw-Hill, 1995), pp. 231-236. This is the text that gave me the idea for this demonstration when I started teaching the senior Theoretical Mechanics course at Kettering University 15 years ago.

[drdanku]

@drdanku Granted, the section in this textbook book is entitled "Fictitious Forces" and the *effective force* observed in the accelerating reference frame has four so-called *fictitious force* terms: Centrifugal force, Coriolis force, Azimuthal force, and Translational force. If the last three of these *fictitious forces* are considered OK, why isn't the first one? Anyone who concedes that the Coriolis force is *real* shouldn't have a problem with a *centrifugal* force in a rotating frame.

[brianburleigh]

@drdanku Thank you for that explanation. Perhaps it is indeed an issue of semantics, but I will concede the "argument" we're having as I've little or no memory of learning non-Newtonian mechanics, or those that involve non-inertial reference frames, and it's clear your knowledge of this subject vastly eclipses my own. Thank you for your explanations and understanding, as well as not calling me an idiot. Cheers!

[drdanku]

@brianburleigh

You need to take some physics beyond the introductory freshman level, like a junior/senior level theoretical mechanics course. Centrifugal forces do not exist when you are discussion the motion of objects in an inertial (i.e., non accelerating) reference frame. However, when you are discussing the motion of objects in a non-inertial reference frame (i.e. a reference frame that is accelerating or rotating), then Newtons' laws of motion no longer apply.

[simondegrootpuntnl]

Great experiment. Thanks for the inspiration.