Sphere Definition and 1000 Threads

A sphere (from Greek σφαῖρα—sphaira, "globe, ball") is a geometrical object in three-dimensional space that is the surface of a ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space. This distance r is the radius of the ball, which is made up from all points with a distance less than (or, for a closed ball, less than or equal to) r from the given point, which is the center of the mathematical ball. These are also referred to as the radius and center of the sphere, respectively. The longest straight line segment through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of both the sphere and its ball.
While outside mathematics the terms "sphere" and "ball" are sometimes used interchangeably, in mathematics the above distinction is made between a sphere, which is a two-dimensional closed surface embedded in a three-dimensional Euclidean space, and a ball, which is a three-dimensional shape that includes the sphere and everything inside the sphere (a closed ball), or, more often, just the points inside, but not on the sphere (an open ball). The distinction between ball and sphere has not always been maintained and especially older mathematical references talk about a sphere as a solid. This is analogous to the situation in the plane, where the terms "circle" and "disk" can also be confounded.

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  1. T

    Minimum force required to form sphere

    Homework Statement Homework EquationsThe Attempt at a Solution Doing a vertical force balance 2Fcosθ=mg ,where m is the mass of water . Not sure how to proceed . What role does the pin hole at the top play ? I would be grateful if somebody could help me with the problem.
  2. T

    Volume Inside a Sphere and Cone?

    Find the volume laying inside x^2 + y^2 + z^2 =2z and inside z^2 = x^2 + y^2. This is a problem my professor made, so I have no way of checking my answer. What I did first was completed the square for the sphere and got x^2 + y^2 + (z-1)^2 = 1, which is a sphere of radius one shifted above the...
  3. C

    Velocity of a Sphere Rolling in a Circular Bowl

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  4. trytodoit

    Proof the shortest path on a sphere is the great circle.

    There are plenty of proofs for the statement, but I do not find one which is not rely on other assumptions. Here are some common proofs of this statement: https://en.m.wikipedia.org/wiki/Great_Circle#Derivation_of_shortest_paths This proof require the path to be differentiable, which is not a...
  5. T

    Moment of Inertia of a Sphere derivation?

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  6. L

    Electric field inside a dielectric sphere with cavity

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  7. Drakkith

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  8. Atlas3

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  9. B

    Point and circle on sphere probability

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  10. W

    Angular Velocity Of A Sphere Rotating Under Gravity

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  11. S

    + charged sphere and - charged sphere touch and separate

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  12. CheesyPeeps

    Sphere on a Flat Plane: 3 Points of Contact?

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  13. S

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  14. U

    Pressure of a sphere on a regular surface

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  15. M

    Calculate No. of Spheres to Cover 50% of a 25m^2 Square

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  16. Alex_Neof

    Calculating the E-Field inside and outside a sphere.

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  17. Y

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  18. Quarlep

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  19. Quarlep

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  20. M

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  21. M

    Electric field on the surface of charged conducting sphere?

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  22. M

    Electric field inside charged conducting sphere?

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  23. C

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  24. C

    Sphere of Uniform Density: Exact Solution to Einstein's Field Eqns?

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  25. C

    Electric charge inside a uniformly distributed sphere

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  26. Estefania_8

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  27. Dethrone

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  28. nuuskur

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  29. J

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  30. P

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  31. LiHJ

    What is the percentage of water in a sphere given its volume and radius?

    Homework Statement Dear Mentors and PF helpers, I can do part (a) and (b) but don't really know how to do (c) and (d). Can somebody teach me how to go about solving it. Homework Equations Volume of cone: $$\frac{1}{3}πr^2h$$ Volume of cylinder: $$πr^2h$$ Volume of sphere...
  32. M

    Equation (with polar coordinates) of circle on a sphere

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  33. M

    Find the weight of a sphere connected to a pulley and to wall

    Homework Statement The system of 2 spheres is in equilibrium. Figure: . If the weight of the second sphere P2=20N, ABC=60 degrees and BAC=30 degrees, find the weight of the first P1 and the force that is applied on the drum of the pulley. Homework Equations P1=m*a The Attempt at a Solution...
  34. R

    Working out a point / segment on a sphere

    Hi, I was hoping someone could help me figure out the problem below. It is a bit of a long winded questions so please bare with me! If you look at Fig 1 below, I have a sphere that spins about an axis in a clockwise direction. (the direction of the spin doesn't really matter) In this case the...
  35. cvex

    How to calculate velocities/forces from sphere collisions?

    Hi, Basically I have a point cloud that represents balls with different radii. They are all moving based on forces and sometimes they are intersecting with each other. Imagine the yellow ball is going in one direction while the blue balls goes in another direction. At one time they are...
  36. A

    Force on a point charge due to a sphere

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  37. H

    Is this possible for hanging objects from spinning sphere?

    This youtube clip has a ride that is a spinning sphere with objects hanging by strings from the surface. (see at about 0:55) This is the only ride in the video I think is theoretically impossible (the others seem like they could be done but would be dangerous and/or costly). I think it's...
  38. Matejxx1

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  39. G

    Electric potential of hollow conducting sphere

    Homework Statement A charge conducting hollow sphere and a point charge with radius of sphere and distancestors between their centers Homework Equations [/B] 3. The atempt at a solution I am unable to find the potential of Shere in presence of external point charge
  40. R

    Prove that a sphere is a conductor.

    Homework Statement How do I prove that a sphere is a conductor? Homework Equations E = kQ/rThe Attempt at a Solution In my mind, if a sphere is a conductor, the charges formed during induction will move to the surface of the sphere as they can move freely in the conductor, and the same...
  41. CARNiVORE

    Velocity of Center of Mass for a Downwardly-Rotating Sphere

    Homework Statement mass = M radius = r rot. inertia = i height = h Sphere of mass M is released from rest at the top of an inclined plane. The speed of the center of mass at the bottom of the incline, without friction, is sqrt(2gh). I need to find the velocity of the center of mass assuming...
  42. W

    Electric Potential V inside nonconducting sphere with cavity

    Homework Statement A nonconducting sphere of radius r_2 contains a concentric spherical cavity of radius r_1. The material between r_1 and r_2 carries a uniform charge density rho_E(C/m^3). Determine the electric potential V, relative to V=0 at r= infinity, as a function of the distance r from...
  43. Aristotle

    Solid Insulator Sphere Inside Hollow Sphere Conductor

    Homework Statement I was looking for some practice problems in my textbook and found this problem that I was just a little stuck on. I drew the diagram from my textbook with the givens of the problem. Homework Equations ∲E*dA = Q (inside) / ɛ0 The Attempt at a Solution For r less...
  44. Dennydont

    Viscosity of liquid for falling sphere viscometer

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  45. H

    Moment of inertia of a solid sphere

    Homework Statement Find the moment of inertia of a solid sphere of uniform mass density (like a billiard ball) about an axis through its center Homework Equations I = ∫rρdV The Attempt at a Solution I =ρ ∫r4πr2dr = ρ4π∫r4 Then I integrate this from 0 (the center) to R, so I = (ρ4π)*(R5/5) And...
  46. D

    Determining the oscillations of an electron within a sphere

    Homework Statement Using an electron as a point particle of charge −e inside a positively charged sphere of radius R ≈ 10^(−10) m and total charge +e, find the density ρ(r) of the positive charge for which the electron oscillates harmonically about the center of the sphere assuming that the...
  47. P

    Electric Flux Through a Hole in a Sphere?

    Homework Statement An uncharged nonconductive hollow sphere of radius 12.0 cm surrounds a 11.0 µC charge located at the origin of a cartesian coordinate system. A drill with a radius of 1.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux through...
  48. S

    Point Charge and Charged Sphere

    Homework Statement A point charge q1 = -6.1 μC is located at the center of a thick conducting shell of inner radius a = 2.8 cm and outer radius b = 4.8 cm, The conducting shell has a net charge of q2 = 2.6 μC. Homework Equations E = (kQ)/r2 F = (kq1q2)/r2 The Attempt at a Solution I honestly...
  49. samjohnny

    Charges inside conducting sphere

    Homework Statement Three fixed point charges of +2 nC, −3 nC and +4 nC are located inside a thin uncharged metal spherical shell of radius R = 2 cm, as shown in the picture attached. Calculate the strength and direction of the electric field at position P, being 10 cm from the centre of the...
  50. T

    A non-conducting sphere, e-field and potential.

    Homework Statement A non-conducting sphere of radius R has volume charge density ρ = B/r. for r<R and ρ = - for r>R. B is a constant. a) Calculate E-field for r>R. b) Calculate E-field for r<R. c) Calculate potential for r>R. d) Calculate potential for r=R. e) Calculate potential for r<R...
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