LKL

Thanks guys! Yes, the OP was about a cheap/easy method for dissolving the material, enzymes and special ionic liquids aren't readily available at the lab but will remain an option if everything else fails. Indeed, one of the problems my mom encountered was the formation of a gelatinous mixture. However, she did manage to prepare a low-viscosity solution by using HNO3 and NaOH, but it had some undesirable qualities. Using HCl and HNO3 before boiling in NaOH sounds promising and she'll look into it as soon as possible. The task isn't as simple as it may seem since the solution has to be run through U/Po ion exchange resins that might have problems with certain compounds/elements contained in grains of wheat. But that's another story...

Any ideas what chemical(s) might be used to completely dissolve a grain of wheat, including the husk. It doesn't matter if the carbohydrates/proteins/cellulose are altered in the process since the aim is to study natural radionuclide levels in foodstuffs (my mother's new job). Any help will be greatly appreciated.

Thanks, swansont. I'd still have some questions though. I've been doing analysis on variable orbits (cycloids) lately. I've especially studied the force exerted on the axis in those situations. The impulse method did seem to work fine if you knew the force acting on the orbiting body/the axis at all times during the cycle. Then it was just simple integration to find out the impulses. They always added up to 0 after a full cycle except in a situation like this. So when the baseball is released, its linear momentum doesn't change, so there should be no recoil impulse on the axel, correct? And when you say that "linear momentum is not conserved", do you really mean this: (linear momentum of baseball in the beginning) + (linear momentum of rod in the beginning) DOES NOT EQUAL (linear momentum of baseball in the the end) + (linear momentum of rod in the end)? And what would be a better tool for this kind of a problem?

The axle will exert a (centripetal?) force on the baseball to keep it in orbit. The baseball will exert an equal and opposite force on the axle. The axle mount will exert a countering force on the axle (since the axle is supported rigidly). So no net force on the axle. Anyway, if we consider the impulse of the force exerted on the axle by the orbiting baseball, it will be 0 after one revolution. You can't get a net impulse by rotation alone, so therefore I3 is still 0. Right? What bothers me is that once the baseball is caught, there will be an impulse to the axle, I2, and once it is released, there should also be an impulse on the axle, I4, according to the previous example. Could you consider the baseball receiving an impulse I5 = -I4 upon breaking from orbit?

"Breaking from orbit" is still causing me trouble... Suppose we have a uniform rod of any given length rotating about its center of mass. For simplicity, let's say that the rod's axle is supported in such a way that all forces acting on it cause only diminutive changes in the velocity of the system. Now, let's say that one end of the rod hits a baseball. Suppose the baseball clings to the rod. Before impact the baseball's velocity relative to the axle was 0, after impact its velocity is Wr (angular velocity*length of rod/2) in the line of the tangent. Let's call the impulse that accelerates the baseball from rest to orbital velocity I1. An equal and opposite impulse will act on the axle, let's call this I2. The baseball will cling to the end of the rod for one full revolution. Since the rod is now rotating about an axis that is not its center of mass, there will be a net force acting on the axle in the direction of the baseball. After one revolution the impulse caused by this net force, I3, will be 0. Once the rod has rotated for one rev, the baseball is let go. According to the previous example in this thread, there should now be a recoil impulse, I4, acting on the axle. But since I1 + I2 + I3 = 0, this would lead to linear momentum not being conserved. So does I4 exist in this situation? Where's the flaw? Help appreciated.

How do you know if that something is spinning or not? What kind of measurements would need to be carried out? I don't know if what I quoted earlier about the non-Euclidean geometry in rotating coordinate systems applies to the "satellite orbiting the 8-ball"- system, since now gravity is causing the acceleration. Differing values of pi should still arise, but there are other differences to the situation. For one, the satellite can't determine whether he's orbiting the 8-ball under its gravitational pull or whether he's in the proximity of a spinning 8-ball with no gravitational field at all. In both cases, an observer inside the satellite would find himself seemingly weightless. In the rotating disc- example, the observer on the disc would find what appears to be his weight related to the distance from the center of the disc. A definite difference here. Yes, by a flywheel I mean just a heavy disc of metal with an axel hole in the center. I = 0.5*m*((radius of the flywheel)^2 + (radius of the axel hole)^2). If you had a flywheel with the axel mounted on the inside rim of a larger wheel, you'd have forced precession by rotating the larger wheel while the flywheel inside it is spinning.

What are the frames that aren't rotating? I don't know much about non-Euclidean geometry, pretty much all of my knowledge stems from the book "Readable Relativity", so I'll just quote some of the main points concerning rotation. Suppose there's a rotating disc, an observer some distance from it(on the same plane) who regards the disk as rotating about its center axis and an observer on the disc. They both consider the other observer rotating about the center axis and so on. It gets interesting when the guy on the disc draws a circle using the center of the disc as its center and goes on to measure its diameter and circumference. When he's measuring its diameter, the outside observer doesn't find his rule contracting. When he's measuring the circumference, however, the outside observer will see the rule contracting. So, they can't agree even on the value of pi. Therefore the disc-stationed observer will live in a non-Euclidean geometry. I guess this would hint at rotation being absolute, since we can all agree on that under non-rotating circumstances our geometry is strictly Euclidean. I'm not certain that the assumption can be made, though. Regarding experimental analysis of precession, how about a forced-precession device? Something that spins a flywheel while at the same time rotating its axis. Might be fun!

Three out of three! Thanks for help.

Sorry, this may be a little off your main point, but the Wolfram article gave me a massice head-ache... What's the physical difference between "rotating objects in stationary coordinate systems, and stationary objects in rotating coordinate systems"? The only one I can think of is that a rotating coordinate system would have a non-Euclidean geometry. Also, what kind of analysis are you doing of precession, purely mathematical or experimental as well?

Think I got it almost solved now, only one conservation law to go! The shifting of the center of mass changes the rotational inertia for the flywheel+counterweight-system only minutely, the new rotational (axis being the center of mass) is 1.47727 kgm^2 as opposed to 1.5 kgm^2 (axis being the center of the flywheel). In the beginning the system's (flywheel + two 1kg weights) total mechanical energy was 8750 J. Once the weight is released, its kinetic energy amounts to 1250 J. Applying the conservation of linear momentum law, the flywheel will gain an opposite velocity of about 4.55 m/s, kinetic energy 113.64 J. Its rotational energy is 7386.35 J, if we assume it's angular velocity doesn't change. Adding up, we get 8750 J. The problem is, since the rotational inertia of the flywheel system decreases and since its angular velocity isn't increased in the process, its angular momentum is not conserved. Could the released object be thought of as having angular momentum even if it's not actually orbiting anything? Any ideas?

Yeah, I'll have to look into this more closely. First time I heard about the parallel axis theorem, dug it up and it looks like tailor-made for this situation. Thanks for help! Please let me know if you stumble across sites that deal with similar situations of "breaking from orbit".

Wow, missed that! The "devoid of external forces" was mainly for simplicity, but I guess if you added a counterweight on the opposite side of the flywheel, ditching one of the weights would now have some sort of a recoil effect on the flywheel+counterweight-system due to the shifting of the center of mass. That's a lot of help already! Any ideas how to calculate the resulting linear/angular momentum changes in the flywheel, while still making the energies match?

Suppose we have a system, devoid of any external forces acting on it, consisting of a cylindrical flywheel (mass 10 kg = mf, diameter 1 m) and an object located on the rim (mass 1 kg = mo), and rotating about a central axis at 100 rad/s = w. Thus, the object would have an orbital velocity of 50 m/s = v. The moment of inertia for the flywheel would be 1.25 kgm^2 = Jf, and for the object 0.25 kgm^2 = Jo. The total mechanical energy of the system consists of the rotational energies of both the flywheel and the object. Etot = 0.5*(Jf + Jo)*w^2 = 7500 J. Now, once the link between the object and flywheel is discontinued, the object will continue moving along the tangent at 50 m/s. If we calculate the kinetic energy for the object, Eko = 0.5*mo*v^2 = 1250 J and the rotational energy of the flywheel Erf = 0.5*Jf*w^2 = 6250 J, we'll notice that together they add up to Etot, so energy is conserved. The question is, what happens to both the angular and linear momentum of the system. If we calculate the situation on the basis of the conservation of energy, it would seem like the total angular momentum decreases once the object is let loose and the system somehow gains linear momentum at the same time. If we calculate the situation on the basis of the conservation of momentum, it would seem like the system gains 2875 J from nowhere, which is clearly impossible! I've never heard of such a thing as transition from angular to linear momentum, but at the moment, I just don't know how to calculate the situation taking into consideration all three conservation laws. Could someone with a little more knowledge in mechanics please help?