Cone Definition and 490 Threads

I need to find the inertia tensor for a uniform thin hollow cone,spinning about its ponted end. When the cone is solid then everything goes very smoothly by using cylindrical polar coordinates. But how should I find if it is a hollow cone. To be able to write the density of the cone I have...

Hi, I have this problem: Compute volume of solid bounded by these planes: z = 1 z^2 = x^2 + y^2 When I draw it, it's cone standing on its top in the origin and cut with the z = 1 plane. So after converting to cylindrical coordinates: x = r\cos \phi y = r\sin \phi z = z...

Before these threads get pushed too far aside (or worse dumped into the bit bucket to make room for more threads), I propose to assemble them together, perhaps in a place like Classic Discussion Threads. They are quite entertaining reading and had me laughing :smile: reading some of our PF...

Imagine that I have a pipe that is on a constant slope at any percent. On the low end of the pipe, there is a container filled with water. The water has naturally found a leveling point up into the pipe. Provided the level of water in the container is above the top of the pipe, a portion of...

What is the shock wave cone half-angle for a supersonic airplane flying at Mach 2.30? Would you use Mach=1/sin(theta) and then divide by 2 to get the half angle? So 2.30=1/sin(theta)=12.9 degrees

Hi , I don't know how to get the edge of the cone in cylindrical coordinates. For example, we have a cone starting at the origin, of heigth 2 and the top is a circle of radius 1 (center at the origin). the edge of the cone is z=2r. but I don't know how they find it. Please can someone...

I am trying to understand this example of finding the center of mass of a uniform solid cone. please refer to the attached figure. We know for obvious reasons that the center of mass will be on the z-axis. I will be referring to the integral that my book used to find the center of mass which is...

I'm an "on-my-own-free-time" arm-chair student of physics. Lol. So if this question is way off the mark my apologies. Feel free to let me know where I’m off base. Anyway... For me, a great visual example of the twin paradox was found at this site...

Thanks to everyones help i was able to understand the center of mass of a cone. Now i have to find the angular momentum along the z-axis as i understand the angular momentum will change as the radius gets larger because the larger radius must spin faster . H = height of cone so the...

I need to find the center of mass of a cone with point facing downwards, of height H and radius R. Since the density is constant throughout and because of axial symmetry the center must be somewhere on the z-axis. I know from convention that this is H/4 but i need to derive this. Rcm...

A circular cone is inscribed in a sphere with a radius of 30cm. The semi vertical angle is theta. Derive a trigonometric equation for the volume of the cone. This has be stumped. I tried looking up proofs for the expression of the volume of a cone for inspiration but all involve calculus.

For a homework assignment i was asked to proof that the positive cone {x^2 + y^2 = z^2, z>= 0} cannot be a submanifold of any dimension of R^3. It apparently goes wrong at the origin. I guess it's because you can't really speak of a tangent space at that point. So I tried to prove by...

volume of a cone is 10 cubic cm... Q: a cone shaped paper drinking cup holds 10 cubic cm of water. We would like to find the height and radius that will require the least amount of paper. Volume of a cone is: (b x h)/3, or with radius is: ((pi r squared x h))/3. I think you solve this...

This is a problem I had in a test and almost everyone got different answers for it, we discussed and well, I spotted mistakes in their solutions so I think mine is right but I wanted to check here and also ask if there is an easier/faster way to do it. There is a container that is similar to...

I have two questions. How do you find the equation of a cone given data points? I've found lots of info on the equation of a cone, but can't find anything on one that is rotated and not centered at the origin. What is the equation for a rotated translated cone? Second, given the equation of a...

Can someone help me with this problem?: We will define a cone in n-dimensions as a figure with a cross - section along its height X_n that has a constant shape, but each of its dimensions is shrunk linearly to 0. a)let D be a cone in R^n with height h (ie. X_n \epsilon...

Hi, I need to find the volume of the solid that lies above the cone with equation (in spherical coordinates) \phi = \frac{\Pi}{3} and inside the torus with equation \rho = 4\sin\phi . I thought that the bounds are: 0\leq\rho\leq4\sin\phi, \frac{\Pi}{3}\leq\phi\leq\frac{\Pi}{2}, and...

We have a right circular cone of base radius a and height a with a uniform surface charge sigma. I want to determine the potential difference between the apex of the cone and the center of the base (this cone doesn't have any charge on the base). My plan of attack for the problem was to...

Hey, im trying to write a program that computes Volume of Intersection of a Cone with a Sphere. Can anyone point me to the math i need to know. Any links, material is good. Thanx

Hi all I have just had what may be an interesting thought. Take a square piece of graph paper, label the horizontal axis "Time" and the vertical axis "Length". We will be using natural units so one grid line in the horizontal axis is one natural unit of time, and one grid line in the...

Hi there, I was hoping that someone here could maybe give me a hand with a couple of issues I'm having to do with moments of inertia. For a right circular solid cone of mass m, height h and base radius a, we have to show that its moment of inertia about a line through its vertex and...

Hello, I have a problem I can't solve. Need assistance! :bugeye: You cut out a piece of a circle (like you cut a piece of a cake), then make a cone by joining the edges of what remains of the circle. What angle must the "cakepiece" have to maximize the volume of the resulting cone? I...

Hi, could someone explain to me the concept and calculation of Solid Angle? I don't think we've actually covered it in our Vector Calculus lectures and I have a question to do on it! Tried searching on the web, but not much information and I really don't understand it. Also, my question is...

FTL travel in a light cone? I read in several places there there is one condition in GR, that will allow you to travel faster than light, and allow time travel to the past. Can someone explain this further, without getting too mathamatical (Ok, maybe a little math). Thanks in advance :smile:

AA loud speaker cone is connected to a AC signal genetator.When the frequency of the signal genetor is alterned the amplitude of the cone changes.why? My working: As the frequency increases the amplitude decreases because there is less change in the magnetic flux and vice versia...I am a bit...

Can there be such a thing as a cone of Ignorance? Can somebody be so ignorant as to drag other people down to their level just by being in close proximity to them? And if this can be so, does that mean that a cone of depression can also exist? Are there any other cones that you can think of?

The area (not including the base) of a right cone is pi*radius*sqrt(height^2+radius^2). What is the area of an inclined cone? (Where the segment joining the tip and the center of the base circle is not perpendicular to the base plane). So what is the area of this, considering we know the...

I am supposed to prove the moment of inertia about a spinning cone through the diameter. but I am supposed to do it using single integration and triple integration. I think I did it right in the triple integration but I really don't know what needs integrating with the single. the paper gave...

this is the entire question: at the shallow end of a swimming pool, the water is 70 cm deep. The diameter of the cone emerging from the water into the air above, emitted by a light source 10.0 cm in diameter at the bottom of the pool and measured by an observer on the edge of the pool 2.5...

Sum-over-histories+Light cone=?! [FONT=Courier New]Is Feynman's sum-over-histories calculated within the light cone? That can't be so, because if all histories are to be "summed", we must include histories in which particles travel at speeds greater than c. This would also be necessary for the...

Can anyone help me with this question? A uniform solid cone of height b and base radius a stands on a horizontal table. Find an expression for the volume of the disc at height h above the base. Integrate over all the discs to show that the total volume, V, is given by V =pi/3 * b * a^2

Can anyone help me with this question? A uniform solid cone of height b and base radius a stands on a horizontal table. Find an expression for the volume of the disc at height h above the base. Integrate over all the discs to show that the total volume, V, is given by V =pi/3 * b * a^2

A conical cup is to be made by joining the edges OA, OB of the sector of a circle of radius 8cm. What angle @ gives the cup of maximum volume? I'm having trouble solving this question. This is what I have done so far we know V=pi*r^2*h/3 r is given, so we need to put h in terms of...

Thanks for taking the time to look at this. I'm getting ready to go to grad school, and I'm realizing that although I did ok in my classes, there are large gaps in my knowledge of physics. That said, I'm currently trying to work my way through an E&M book, and now I'm stuck. Here's the...

If I have a cone and divide it into infinately small slices. Wouldn't both sides of one slice have the same area and wouldn't the next slice (and so on) have the same area as the slice before. So wouldn't your cone actually be a cylinder? My answer is no, because the reasoning is wrong. If I...

I am working on a rocket and need to find the center of mass of a hollow nose cone. Any help would be appreciated.

I don't know if anyone will be able to help me, I am really stuck on this question! "Show that the volume of the region bounded by the cone z=sqrt((x*x)+(y*y)) and the parabloid z=(x*x)+(y*y) is PI/6" The bits in the brackets (ie x*x and y*y) are x squared and y squared respectively and...

A right circular cone is inscribed in a hemisphere. The figure is expanding in such a way that the combinded surface area of the hemisphere and its base is increasing at a constant rate of 18 in^2 per second. At what rate is the volume of the cone changing when the radius of the common base is 4 in?

Time is on the y-axis and distance is on the x-axis and z-axis. Depending upon your velocity the cone is formed. At, let's say 1/10c, you can reach point "A" in ten years and your cone is narrow, but at 1/5c point "A" is 5 years away and the cone is wider. At 1/2c you could be at point "A" in...

I'm in the process of designing a scoop used for automotive purposes. Anybody know some formulas pertaining to pressure, velocity and area dealing with scoops (Funnels, cones, etc)? Thanks for the help! Joe