Science Student

2 metal disks are welded together. One has a radius of R1 = 0.025m with a mass of m1 = 0.80kg and the other has a radius of R2 = 0.05m with a mass of m2 = 1.60kg. A light string is wrapped around the edge of the smaller disk. At the end of the string is a block with mass mb = 1.50kg. The block is released y = 2.00m from the ground. What is the speed of the block just before it strikes the ground? U(1) + K(1) = U(2) + K(2 U(1) + 0 = 0 + K(2) U(1) = mbgy K(2) = (1/2)mb(v^2) + (1/2)(I)(w^2), where I = (1/2)(m1) (R1)^2 + (1/2)(m2) (R2)^2 = 0.0025kgm^2, and w^2 = (v^2)/(R1^2). mbgy = (1/2)mb(v^2) + (1/2)(I)(w^2) 2mbgy = mb(v^2) + (I)(v^2)/(R1^2) v^2 = (2mbgy)/(mb + (I/(R1^2))) v = 3.27m/s But the answer in the textbook is 3.40m/s. The textbook seems to never be wrong. Does anyone see anything wrong with my work?

Thank-you very much, you are very generous with your time and knowledge.

Okay thanks, I am still unsure about all of this.

When finding the moment of inertia, I was taught that the procedure is to use a constant P for uniform density to equal a derivative of mass over a derivative of volume, dm/dV. And we know that P also equals all of the mass over all of the volume. This seems to mean that the ratio dm/dV equals the ratio m/V. But dV for a cylinder equals 2(pi)*r*h*dr which does not quite equal the volume (pi)(r^2)*h. Or do ratios of infinitesimals to real values work differently than real ratios to real ratios? If so, how?

Thanks!

Is the interval a fixed height?

I am not in multivariable calculus yet, but I am going crazy trying to create the formula for a cylinder by integration, not a homework assignment. I can't put h in terms of r; is there another way to do this using single variable calculus? If the answer is no, then is the inability to put one variable in terms of the other mean that I must use multivariable calculus?

There are no excuses not to accomplish anything that is physically possible.

Fighting for survival is natural too.

Most people pursue financial gain. What if we all sought biological gain? The latter makes more sense to me. We are approaching technology that will allow for us to have control over our own mortalities. Shouldn't this be our highest priority? I have a very wealthy friend who makes a high income in finance. His job is to convince banks to loan wealthy people money interest rates that make my friend and the bank high profits. When I visited him, he took me on his expensive boat. We had a pretty good time, but I think he said that he used up about $1000.00 that day in fuel. Then we went back to his mansion. Only about 15 years ago, we would amuse ourselves with simple games like Monopoly and Risk when money was tight. However, we both agree that we had plenty of fun back then. I couldn't tell him this, but I am sure we had more fun playing cards and board games than being on his boat. My point is simple and probably obvious. Excessive money may or may not make life "better". If it does, I have yet to discover hard evidence for this. One thing that we can all probably agree on is that life is more important than money. Without life money has no value. Money cannot buy life yet, generally. The only thing that can gain life for people is to learn how to increase time alive; and by "time" I mean quality time. We live in a universe that has told us its building blocks. It is not a matter of can we live as long as we want but a matter of how. So what if I asked my friend and every other person like him to go back to school and study biotechnology, which encompasses practically all of the sciences? He will say "no". But how can I make him and people alike to understand that their priorities don't make sense? If we all help advance medicine to the point where we can live as long as we want, we can have boats later. The positive scientific articles and research on reverse aging and cures for diseases are so plentiful that I wouldn't even know where to start selecting them to support my contention for this topic. I can't help but ask again, how can I get this point across to the masses like my friend? I have come to this forum hoping to read some ideas.

Yeah, this the first semester of first year physics. It seems to be an introduction to finding inertia by using integration.

Sorry for the confusion, I really just want to know what dV actually means for cylinder with uniform density and fixed dimensions. I think that the textbook wants us to assume the values for the dimension are fixed but equal L, r, P,V just to get a general formula for the inertia of any cylinder. However, the book does want r to vary when integrating the infinitesimally thin shells of the cylinder as they need to change in circumference.

I know that the volume of a cylinder is V = (pi)*L*r^2. But, when it comes to dV of cylinder, my book seems to imply two different answers. On one page of my textbook dV = dx*dy*dz, where x, y and z are the three dimensions; okay that makes sense. But then when it explains how to find the moment of inertia of a solid cylinder, it suggests using dV = 2*(pi)*L*r*dr to put the differential and integration variables in the same terms, which also makes sense. But now we are using a derivative of only one dimension while r and L are its actual values. So the explanation of dV has all 3 dimensions differentiated. But in the problem, they only differentiate one of the dimensions. Does anyone know how dV can mean two different things?

These are my own questions to make sense of the corollary. Unfortunately, my professor does not seem to think that additional information is needed for the not-so-genius math students. Thank-you so much!

Here's the corollary: Let X be a nonempty set and f : N×X → X be a function. For each x ∈ X there exists a unique sequence x(1), x(2), ... such that x(1) = x and x(n+1) = f(n,x(n)). Question 1: What exactly does x(1) = x mean? In the same context, what would x(2) equal? Question 2: What does the second part of this equation mean x(n+1) = f(n,x(n))? Is it an ordered pair for an x-y graph or...?

The greedy nature in me wants to live in a mansion, but we don't always have to get what we want. Maybe they could play some violent video games.

I am mostly interested in what may be the result if my idea in the OP actually happened.

It was just an example to show that my idea might be possible.

You are arguing about things that I didn't even say, such as "many nations". And then you added "as a whole" when I was not referring to military capabilities as a whole. So I am going to stop this conversation with you.

My point was that there has been a collaboration that involved nations agreeing to weaken military capabilities. No, it was too stupid for words. My post was responding to iNow's post.

I strongly disagree. The U.S.A. and the U.S.S.R. agreed to curtail the production of nuclear arms and reduce their stockpiles, http://en.wikipedia.org/wiki/SALT_II#SALT_II . My example is way too vague. I meant something else. There are many things that many people want and don't want. But we can all agree on two things that we want at least for ourselves; the two things are health and life.

Can you give me a reason or reasons why a country wouldn't want to participate in such an agreement? What I feel that I have designed is a win-win proposal where no country loses in such an agreement but only gains. Imagine you square off with somebody in a street fight because of an argument or whatever. But before you fight, someone offers you both $1000.00 each to simply move the fight closer to a crowd where the guy can raise the money. So, you both are going to beat each other up, but you will both gain/win in a different way. So one person loses the fight but receives money, and the other person wins and receives money. This is a synergy of benefit - if you will. It is a win-win proposition to move the fight. That seems like a good idea. The fact that big pharma won't touch DCA (a good cancer curing prospect) tells me that your idea needs to be implemented. And if it is already implemented to some degree, then the current model is not good enough. And, I agree with everything else that you said.

That could be what Phi meant. Or maybe Phi meant pharmaceutical companies. If Phi meant that, then I can see the point. In Canada the process is that the universities first discover something, and then bid pharma buys patenting for it and then invests money into it for further research and development like clinical trails, marketing etc. But a huge and interesting problem is that they are not interested in one-time cures as much as they would be interested in something that requires indefinite usage. They also need it to be patentable. An example of this is http://www.cancer.ca/en/about-us/news/national/2013/canadian-cancer-societys-perspective-on-dca/?region=on DCA is not patentable, so big pharma has no interest in it, which makes sense from a business perspective.

Why would the money have to go to private businesses? Why can't it keep going to universities or government funded medical research organizations? If more money went to education for medical research, then I would consider that a way to support medical research.

That doesn't make any sense to me. This is a gain for China and every other country. Ideally, nothing changes militarily if every country makes fair cuts; they will only gain by advancing medicine for human beings.