Conical Definition and 140 Threads

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the lateral surface; if the lateral surface is unbounded, it is a conical surface.
In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, it extends infinitely far. In the case of lines, the cone extends infinitely far in both directions from the apex, in which case it is sometimes called a double cone. Either half of a double cone on one side of the apex is called a nappe.
The axis of a cone is the straight line (if any), passing through the apex, about which the base (and the whole cone) has a circular symmetry.
In common usage in elementary geometry, cones are assumed to be right circular, where circular means that the base is a circle and right means that the axis passes through the centre of the base at right angles to its plane. If the cone is right circular the intersection of a plane with the lateral surface is a conic section. In general, however, the base may be any shape and the apex may lie anywhere (though it is usually assumed that the base is bounded and therefore has finite area, and that the apex lies outside the plane of the base). Contrasted with right cones are oblique cones, in which the axis passes through the centre of the base non-perpendicularly.A cone with a polygonal base is called a pyramid.
Depending on the context, "cone" may also mean specifically a convex cone or a projective cone.
Cones can also be generalized to higher dimensions.

View More On Wikipedia.org
Recent contents Top users
  1. B

    Optimization question - water in a conical tank

    Homework Statement A water tank is in the shape of an inverted conical cone with top radius of 20m and depth of 15m. Water is flowing into the tank at a rate of 0.1m^3/min. (a) How fast is the depth of water in the tank increasing when the depth is 5m? Water is now leaking from the...
  2. S

    Conical Pendulum: Get Help Now!

    HELP ME i tried spliting the forces of the tension of the string but I don't know how exactly
  3. C

    Conical Pendulum: Mass, Speed, Frequency & Trajectory Explained

    Conical Pendulum--- did I do this right? Homework Statement A ball is attached to a string with length of L. It swings in a horizontal circle, with a constant speed. The string makes an angle (theta) with the vertical, and T is the magnitude of the tension in the string. 1)Determine the...
  4. W

    Understanding F=ma: How to Prove It with Conical Pendulum Equations"

    It's not a problem, it's a proof. The trouble being that I'm not entirely sure what I'm supposed to be proving, which is why I'm getting so confused. Our instructor told us to verify F=ma using the equations that we got from a conical pendulum lab. When further prompted, he said to divide them...
  5. B

    Why is the speed of a particle in a conical pendulum related to the angle theta?

    Homework Statement A particle is suspended from a fixed point by a light inextensible string of length a. Investigate 'conical motions' of this pendulum in which a string maintains a constant angle \thetawith the downward vertical. Show that , for any acute angle theta ex], a conical...
  6. D

    What is the Effect of Angular Acceleration on a Block on a Conical Surface?

    http://img357.imageshack.us/img357/6476/80028206ag6.gif This question had me a little confused. I started by drawing a free body diagram of the block: http://img246.imageshack.us/img246/9121/59804825wo9.gif Where W is the weight, N is the normal force and F is the friction force...
  7. Y

    Can a flying pig float in water like a conical pendulum?

    I have a question about the flying pig. A flying pig is just a toy pig with wings that is hung from the ceiling with a string. When you turn it on, it flies in a circle and shows concepts of conical pendulum. But it only flies in one direction. If you push the pigs in the opposite direction...
  8. Y

    Conical Pendulum: Physics Behind Its One-Way Motion

    When you hang a pendulum from the ceiling and spin it, (conical pendulum) why does it only spin in one direction? What's the physics behind the motion and the forces of it that makes it spin in only one direction?
  9. T

    Calculating Conical Acceleration for a Rotating Object on a Table

    Homework Statement A light string can support a stationary hanging load of 25.0 kg before breaking. A 3.60 kg object attached to the string rotates on a horizontal, frictionless table in a circle of radius 0.800 m, while the other end of the string is held fixed. What range of speeds can...
  10. S

    Conical Pendulum Homework: Determine Force, Find Radial Acceleration

    Homework Statement Consider a conical pendulum with a 81.0 kg bob on a 10.0 m wire making an angle of theta= 2.00° with the vertical. (a) Determine the horizontal and vertical components of the force exerted by the wire on the pendulum. (b) What is the radial acceleration of the bob...
  11. M

    Deriving Shear Stress on a Conical Bore Fluid Element

    I would like to derive a relation for shear stress on a conical bore shaped fluid element. Essentially, I have flow going through a converging nozzle. I know variables in this include length of the nozzle, inlet and outlet diameters and pressures and nozzle angle. I've done a force balance on...
  12. M

    CENTER OF MASS of a circular conical surface

    Homework Statement Find the center of mass of a circular conical surface (empty cone) of height H. Homework Equations z(CM) = 1/M * int(z*dm) x(CM)=y(CM)=0 (we've taken the origin of coordinates at the center of the base) The Attempt at a Solution This problem far exceeds my...
  13. T

    Conical Pendulum: Period and Tension Calculation

    Homework Statement Conical Pendulum Question Mass (m) is attached to the ceiling by a String of Length (s) The string makes an angle of (\theta) with the vertical Compute the Period of Revolution and the Tension in the string? Mass of Bob (m) -- 4.35kg Length of String (s) -- 5.50 meters...
  14. P

    What Are the Force Components and Radial Acceleration in a Conical Pendulum?

    Homework Statement Consider a conical pendulum with a 78.0 kg bob on a 10.0 m wire making an angle of θ = 5.00° with the vertical. (Consider positive i to be towards the center of the circular path.) (a) Determine the horizontal and vertical components of the force exerted by the wire on...
  15. S

    Conical problem finding tensions and periods

    A "conical pendulum", in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.060 kg, the string has length L = 0.90 m and negligible mass, and the bob follows a...
  16. C

    Speed of Block 3.5s After Start Moving | Conical Pendulum

    A 3.46 kg block located on a horizontal floor is pulled by a cord that exerts a force F = 13.9 N at an angle theta = 26.0° above the horizontal, as shown in the Figure. The coefficient of kinetic friction between the block and the floor is 0.09. What is the speed of the block 3.5 s after it...
  17. P

    Solving Conical Pendulum Problem: Results & Tips

    i was solving thsi problem and attempted it in this manner consider a length dx of the rod at a distance x from the pivot now let \theta be the required angle dx\cos\theta = dm g dx\sin\theta = m\omega^{2}x\sin\theta dividing we get \tan\theta = \frac {\omega^{2}x\sin\theta}{g} which is...
  18. M

    Angular Momentum of a conical pendulum

    Homework Statement A small metallic bob is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread describes a cone. Given: Length of string = 2.8m Angle between string and vertical: 21 degrees...
  19. M

    Conical Pendulum Homework: Find Ratio of Tangential Speeds

    Homework Statement Consider 2 conical pendulums. The first one has mass M and length L and the second has mass 4M and Length 4L. For both parts the angle theta is 33 degrees. The ratio of the tangential speeds of the two circular motions V2/V1 is? Homework Equations I know that...
  20. H

    Calculating Inclination & Time of Revolution for a Conical Pendulum

    1. The string of a conical pendulum is 1m long. An initial speed of 3m/s causes the bob to describe a horizontal circle. Find the inclination of the string to the vertical and the time of revolution. The answers at the back give 50.1 and 1.6s I'm trying to find the angle that the string makes...
  21. C

    Solve Conical Pendulum: Find Speed, Period, Horiz. Comp., Rad. Accel.

    The Conical Pendulum A small object of mass m is suspended from a string of length L = 1.8 m. The object revolves in a horizontal circle of radius r with constant speed v and angle = 28° Find the speed of the object. i found s=v=2.098. Find the period of revolution, defined as the...
  22. F

    What Is the Angle Between the String and the Vertical in a Conical Pendulum?

    Homework Statement A mass m= 4.7 kg is suspended from a string of length L=1.19m. It revolves in a horizontal circle. The tangential speed of the mass is 2.97 m/s. What is the angle between the string and the vertical (in degree.) Homework Equations r= Lsin(theta) Tension is broken up...
  23. B

    Rate of change: Height of a conical pile

    The problem states: sand falls onto a conical pile at a gravel yard at a rare of 10 cubic feet per minute. The base of the pile is approximately three times the altitude. How fast is the pile getting taller when the pile is 15 feet tall?Volume = πr² h/3 dV =...
  24. T

    Why did my force analysis for a conical pendulum problem yield the wrong answer?

    I tried to do this pendulum problem with force analysis, but I kept getting a wrong answer. Eventually I figured it out using torque, but I still have no clue why I was getting a wrong answer when I try to use f=ma. Any help appreciated! Homework Statement A conical pendulum, a thin uniform...
  25. J

    Related Rates and a Conical Tank

    A water tank is in the shape of an inverted cone with depth 10 meters and top radius 8 meters. Water is flowing into the tank at 0.1 cubic meters/min but leaking out at a rate of 0.001h2 cubic meters/min, where h is the depth of the water in the tank in meters. Can the tank ever overflow...
  26. A

    Is the Clem Conical Pump Engine Actually a Functional Machine?

    I have found a few sites that contains plans for a hydraulic engine that could run itself for a total of nine days. http://www.rexresearch.com/clemengn/clemengn.htm" http://www.keelynet.com/energy/clemindex.htm" Would it be practical to use this as an engine.
  27. mbrmbrg

    Tension in a conical pendulum's string

    The problem: Figure 6-43 shows a "conical pendulum", in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.050 kg, the string has length L = 0.90 m and negligible...
  28. W

    Conical Pendulum Problem -Right Way of Solving?

    Hello, I wanted to make sure that I am solving this problem in the correct manner, because one of my answers seems a little off from the book's. "Consider a conical pendulum with an 80.0-kg bob on a 10.0-m wire making an angle of 5.00(degrees) with the veritcal. Determine (a) the horizontal...
  29. D

    Conical Pendulum: A Level Maths Required?

    i know this isn't exactly homework, but i couldn't find anywhere else to put it! we've been doing s.h.m. in physics, and when we considered a simple pendulum my teacher mentioned that you can also have a conical pendulum, but the maths for it is more complicated. i want to know more about this...
  30. R

    Parabola conical whatever equations

    I am dazed and confused how does 2x^2=y end up being directrix y=-1/8?
  31. S

    How to Solve for CosA and T in a Conical Pendulum?

    Hello all , I encouter a problem solving this one : We are given a conical pendulum with : V - tan. speed of particle m - mass of rotating particle g - gravity acceleration...
  32. P

    How to Solve a Conical Tank Calculus Problem

    I have a calculus question and was wondering if some could help me see what I am doing wrong in this question. Thank you A conical tank with an altitude of 10m and whose base has a radius of 4m is mounted with its vertex down. The tank is full of water which is draining through the vertex...
  33. T

    Learn Conical Coordinates with Mathworld

    Anyone here can teach me the conical coordinates? I tried reading it in mathworld, but didn't understand it, anyone can give me the direct transformation, jacobian, some transforms and use of it?
  34. M

    Effective resistance of truncated conical cylinder

    Hi, I'm having trouble doing this problem: A truncated conical cylinder of graphite (bulk resistivity \rho = 1/\sigma ). The top of the cylinder has radius r = a, the bottom has r = b (b>a). Find the effective resistance between top and bottom of the cylinder. Show that the expression reduces...
  35. Reshma

    Simple pendulum, a conical pendulum and a compound pendulum?

    What is difference between a simple pendulum, a conical pendulum and a compound pendulum? In which category does a Foucault's pendulum fall in?
  36. D

    Conical Pendulum, Mass and Period

    Hello. I am having trouble understand the varying mass's effect on the period of a conical pendulum. Well, I understand that there is no effect. However, I am having trouble verifying that in a centripetal force equation for circular motion. Most generally, conical pendulum's centripetal...
  37. P

    Music: conical vs cylindrical instruments

    a flute is cylindrical and when you hit the 2nd register (higher notes) the fingering is pretty much the same as on the base register. in other words, the jump is a regular octave. a clarinet is conical and the jump to the 2nd register is a 12 note jump from what i understand. can anyone...
  38. Q

    Solving [problem2.26]: A Conical Surface's Potential Difference

    I have a problem from Griffiths Introduction to EM [problem2.26] A conical surface (an empty ice-cream cone) carries a uniform surface charge <sigma>. The height of the cone is h, and the radius of the top is R. Find the potential difference between points a(the vertex) and b (the center of...
  39. Another God

    Water Pressure in Conical Tank Question

    I was wondering if anyon could help me out. You have a conical tank with a top diameter of 1m, going down to an outlet of 150mm diameter, height of the tank = 3m, and it's full of water. Assuming an air pressure of 15psi, what is the pressure at the 150mm opening? (the bottom)? Does the...
  40. G

    Solve Physics Problems: Moon, Sun, Springs & Conical Mound

    Someone please help me how to do these problems below. Thanks a lot for your help. 1) On the surface of the moon the acceleration due to gravity is approximately 1/6 the sun at the surface of the earth, and on the surface of the sun it is approximately 29 times as great as at the surface of the...
Back
Top