# Homework Help: Centrifugal Vertical Tangential Inertia?

1. Nov 22, 2005

### kliide

Hi, first post. I'm a math/physics, uh, underachiever and I'm looking for more resources on Centrifuges. I apologize in advance for the inaccuracy of my use of physics terminology.

I'm interested in finding a formula that calculates both the amount of force and angle of force of tangential inertia in a centrifuge. I've found many explanations involving centrifuges where the tangential inertia is restricted to 2 dimensions and described in terms of the tangential inertia created by rotary motion, but only on a horizontal plane.

Here's my problem: what I'm trying to find out is how tangential inertia would apply in a 3 dimensional system where the rotating mass was fixed to the central hub below the height at which the rotating mass' center of gravity/mass would be optimally distant from the center of the rotating mass. I guess what I'm trying to describe is like a pole with 2 tether balls attached by equal length strings.

Just from observation, I can see that once the pole begins rotating at an appropriate speed, the tether balls are pulled outward until they lie on a plane with the point at which they were fixed. I'm guessing that in this case the vertical trajectory would curve with the radius of the string until reaching a point on a plane with where they were tethered to the pole. I'm also guessing that the tangential inertia would be restricted to a 2 dimensional horizontal plane and the vertical component of movement was only a result of being fixed by a string.

Ok, now for the actual question. If the tether balls were fixed at a 45 degree angle below the plane at which they were fixed to the pole (using a steel rod instead of string), what would the resulting angle of tangential inertia be in this configuration? Is there a vertical component to the inertia in a centrifuge arrangement where the center of gravity/mass of the rotating mass lies below the point at which the rotating mass is fixed to the pole? If there is a vertical component to this inertia, then how is it defined?

Jon

2. Nov 23, 2005

### kliide

question fixed (?)

Ok, I can see why no one will reply to this post. The question is really cluttered. Also, right after posting the question, I think I kind of figured it out. I guess putting the question out there really is half the battle :)

1st, there's no 3 dimensional diagrams of centrifugal inertia because it only ever operates in 2 dimensions: outward from the center of the rotating mass (z, and x).

2nd, the vertical component of the movement that I observe, although the result of inertia, does not itself suggest vertical inertia. The vertical movement of the tether balls is a result of structural tension/compression of the string/steel rods resulting from the tether balls being pulled/pushed outward to points on a plane that are optimally distant from the center of the rotating mass.

That being said...did I answer my question? I feel like I did, but maybe it's the quality of the instant coffee I've been drinking that leaves me in doubt. Could someone please verify that, aside from coriolis inertia, I've accounted for most of the major fields/effects that act upon this arrangement?

Oh, and another question came about when I was looking for answers to this question. I came across Accelerated Frames of Reference, Huygens, Einstein and other stuff that has created pressure on the inside of my skull along with possible hemorrhaging. Why does the frame of reference have to be some fixed frame like the cosmos or whatever? Can't the fixed frame of reference simply be the axis about which the tether balls are spinning? I know in the example of a pole you could say the tether balls might be still while the pole was spinning about its Y axis. But what about an electric motor in some kind of non-space ether without an external frame of reference? If you attached tether balls to both the motor and the axle, wouldn't you be able to determine what was spinning and what wasn't, by observing whether centrifugal force acted upon the tether balls attached to the axle OR the motor? Or would the whole thing just gain a double spin? The axle goes clockwise, while the motor goes counter clockwise and BOTH sets of tether balls are spun outwards? Ugh...

Jon

3. Nov 23, 2005

### Chi Meson

You are indeed all mixed up in the words you are using. Please stop trying to "make up" physics as you go, and try one more time to ask the question you want to know the answer to.

By the way, there is only "inertia." There are no componants to inertia. Inertia is not a force, it is the tendancey of things to continue in a straight line at a constant speed (if they are already moving) or to stay at rest (if they are not moving). Understanding inertia is half the battle.

The second half is to understand that as you watch the tetherballs, there is NO "centrifugal force" that pulls them outward. NOTHING pulls them outward. At any moment in time, they are trying to continue in a straight line, but an inward force causes them to change direction and move in a circle.

4. Nov 24, 2005

### kliide

Another attempt at rephrasing my question.

Well, for one..I never said there WAS a centrifugal force. I guess I had difficulty describing the motion of the tether balls outwards from the axis of rotation..I guess I could have said, uh, impelled? What's the proper verb to describe the action of inertia on a mass anyway? Inerted?? So, apologies for resorting to saying pushed/pulled...once (*edit* ok, twice). Argh, I used those darn verbs twice, and suddenly inertia is a force in my eyes and my use of Tangential Inertia as a term is totally disregarded. And by Tangential inertia, I was just referencing the term as it was used elsewhere when discussing centrifugal inertia.

As for "making up" physics...I think a more accurate phrase would be "developing an understanding of physics". I thought that, by forming my question in, well, the form of a question, I would have made it clear that I was trying to clarify things for my understanding rather than trying to develop a "new" physics for YOU to understand. What did I make up, anyway?

Anyhow, that being said. When I mentioned "components" I kept that term within the context of physical translation along 2 or 3 dimensional space (i.e: "outward" component, "vertical" component), so I wasn't suggesting an actual physical object, just elements that describe physical space. Since inertia, as you say, is the tendency of an object to continue along a straight line in constant speed, then the straight line is a spacial translation which can occur in 3 dimensional space. My use of "component" was my layman way to differentiate different axes of directional space. Since a component is defined as a constituent element of a system, certainly the vertical, horizontal and depth axes of a spacial coordinate system could be considered constituent elements of a spacial coordinate measurement system. I hope that misunderstanding has been cleared.

So, to rephrase the question... Why and how does a tether ball, tied to a pole, move upwards when I hit it sideways? I expect you'd answer: because the tether ball's inertia pulls/stretches the string outwards (yea, I know I said pulled, but in this context it is completely accurate).

My confusion lies in whether or not the inertial tendency of the tether ball is altered in anyway by the vertical course it is forced to take by the string. Since the mass of the tether ball is now moving upwards, wouldn't that mean that the inertial direction has also been altered? If so, then to what degree?

Thanks again,
Jon

Last edited: Nov 24, 2005
5. Nov 25, 2005

### kliide

There's been a lot of clutter in this thread due to my "thinking out loud"..so I'll put up a final post that hopefully provides a clear question for someone to consider. Apologies for the garbarge above.

Here's the revised question again:

The setup: There is a 1 kilogram orb, attached to the bottom of a 10cm long massless rod. The top of the rod is attached to a hinge that is located at the top of a 15cm vertical stand. The hinge (and rod) is locked at an angle 60 degrees away from the vertical stand. The vertical stand is positioned on top of a turntable. The turntable is rotated at 1000rpms (circumference of turntable is 100cm).

Question: How do I calculate the strength and direction of inertia at the center mass of the 1kg orb?

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Do I just calculate the inertial tendency in planar xy, then planar xz and then use the "parallelogram law" to determine the vector of the inertial tendency ?

I'd actually prefer the formula(e) required to figure this out. Honestly, there's some other things I need to know before I can become adequate at the calculation of physics formulas, but I would use your input as future reference for a time when I get my head around the math side of things.

Thanks,

Jon

Last edited: Nov 25, 2005