What is Hemisphere: Definition and 159 Discussions

The Western Hemisphere is a geographical term for the half of Earth which lies west of the prime meridian (which crosses Greenwich, London, United Kingdom) and east of the antimeridian. The other half is called the Eastern Hemisphere. In geopolitical terms, the context in which the term is most often used, the Encyclopedia Britannica defines it as "North and South America and the surrounding waters. Longitudes 20°W and 160°E are often considered its boundaries." It may be used in a cultural or geopolitical sense as a synonym for the "New World".

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  1. gracy

    Electric flux through a hemisphere due to these charge configurations

    Homework Statement The figure shows a charge q placed at the centre of a hemisphere. A second charge Q is placed at one of the positions A,B,C and D .in which position(s) of this second charge , the flux of the electric field through the hemisphere remains unchanged ? 2. Relevant Point: My...
  2. yango_17

    Manually integrating to find flux through hemisphere

    Homework Statement Basically, I am being asked to calculate the electric flux through the top of a hemisphere centered on the z-axis using "brute force integration" of the surface area. Homework Equations Gauss' Law The Attempt at a Solution Using intuition and Gauss' law, I know that the...
  3. Adoniram

    Center of Mass of Hemisphere

    Homework Statement Find the center of mass of a hemisphere of radius R. Homework Equations R_cm = (rho/M) Integral[ (vector r) dv] dv = r^2 Sin[theta] dr d[theta] d[phi] The Attempt at a Solution [/B] In spherical polar coordinates, vector r = r r-hat, so the argument of the integral should...
  4. Kior

    Why is there a seasonal cycle of CO2？

    I am preparing my AOSS class next semester, and I found it is interesting that there is a seasonal cycle of CO2. I looked for some information on the Internet, and this seems to do with the plants. They awake in the spring and summer, absorbing a lot of CO2 by photosynthesis and die in the...
  5. J

    Electric Field due to Shell Hemisphere

    Homework Statement Calculate the Electric Field generated by a hemisphere of radius ##R## (and uniform charge density ##\sigma##) at its center. Homework Equations ##\displaystyle E = \frac{Q}{4\pi \varepsilon_0 r^2}## The Attempt at a Solution I think I'm doing some mistakes with the...
  6. M

    Centre of mass of a solid hemisphere. What am I doing wrong?

    I have to calculate the centre of mass of the drawn hemisphere. I don't understand where I make mistakes. The process I followed on the above image is the following: (I) Here I simply translated position vector components from cartesian to polar coordinates. (II) Formula of x-component of...
  7. B

    Thermal expansion (Simple) (attempt posted)

    Homework Statement I'm looking for a good explanation, not interested in the answer. A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 on a winter day at a temperature of -18 C. How much more interior space does the dome have in...
  8. AdityaDev

    Acceleration due to gravity at the centre of a hemisphere

    Homework Statement find the acceleration due to gravity at the centre of a solid hemisphere. Homework Equations ##F=\frac{GMm}{r^2}## The Attempt at a Solution i decided to go for cylindrical coordinayes (which is way beyond my syllabus). I did some research though. let me take a point...
  9. dodonaomik

    Please find the force Fz which the hemisphere endures

    Homework Statement My English of influid meachanics is poor, so I only can hope that you can understand the figure (please forgive me!) Please find the force Fz which the hemisphere endures Homework Equations My way: "on" the hemisphere, I want to use triple integral（but I'm not sure...
  10. W

    Where is the Center of Mass in a Solid Hemisphere?

    Homework Statement Consider a solid hemisphere of uniform density with radius R. Where is the center of mass? z=0 0zR2 z=R2 R2zr z=R Image is provided. Homework EquationsNoneThe Attempt at a Solution Answer A and E do not seem logical. I thought it was answer C from my eyes. Center of...
  11. J

    Solid hemisphere resting on an inclined plane

    Homework Statement A solid uniform hemisphere rests in equilibrium with its curved surface in contact with a rough inclined plane which is elavated by an angle α where sin(α) = 3/16. Find the angle between the symmetry axis of the hemisphere and the vertical.[/B]Homework Equations Sine rule...
  12. F

    Center of mass of hemisphere: substitution of z=rcos(θ)?

    Homework Statement I am trying to understand a substitution used to solve for the center of mass of a solid uniform hemisphere as in this post: https://www.physicsforums.com/threads/solid-hemisphere-center-of-mass-in-spherical-coordinates.650663/#post-4151797[1] I completely understand the...
  13. J

    Particle constrained to move on a hemisphere

    Homework Statement A particle slides on the outer surface of an inverted hemisphere. Using Lagrangian multipliers, determine the reaction force on the particle. Where does the particle leave the hemispherical surface? L - Lagrangian qi - Generalized ith coordinate f(r) - Holonomic constraint...
  14. D

    Block slides down hemisphere; time to leave surface?

    A block is at rest at the top of a frictionless hemisphere of radius r. It is slightly disturbed at starts sliding down. I already know where it will leave the surface (height = 2r/3). My question is, WHEN will it leave the surface?
  15. G

    Finding electric field of a hemisphere (without using Gauss' Law)

    Homework Statement A charge distribution is given by ##\rho(r,\theta,phi)=\gamma r^3cos\theta,a<r,b,0\leq\theta\leq\pi/2## and is zero everywhere else. The distance from the origin ##r=\sqrt{x^2+y^2+z^2}## and ##\gamma## is a constant. Write out the electric field P along the z-axis a distance...
  16. N

    Hemisphere meshing quad in ansys

    Can anyone guide me how to mesh solid and shell 3d hemisphere with hex dominant approach in ansys mechanical APDL? I found no such verification manual for 3d hemispherical meshing in ansys. What method should be applied and what element should be chosen appropriately to mesh this structure? I...
  17. matineesuxxx

    Block Sliding Down Hemisphere

    Homework Statement A block of mass m slides down a hemisphere of mass M. What are the accelerations of each mass? Assume friction is negligible. (See attatchment) Homework Equations a_M = Acceleration of hemisphere N_m = Normal force of M onto m N_M = Normal force of ground onto M...
  18. B

    How do I integrate a hemisphere using spherical coordinates?

    Integrating a hemisphere Homework Statement I am self-teaching calculus. I'd like to integrate a hemisphere G (http://en.wikipedia.org/wiki/Spherical_cap), where the points of each circle have a given property (k=100x/(√20x)3 the radius of G r = 10, A = 628.3, h = x the top point is A...
  19. J

    Why does a spinning hemisphere right itself?

    I noticed this intriguing phenomena whilst messing about in work with a perfect glass hemisphere the other day: Place the hemisphere on a surface, with the flat surface facing upwards. (Looks like a 'D' rotated 90 degrees clockwise). When I spin the hemisphere fast enough, it will spin...
  20. D

    Radius of circular impulse wave in the hemisphere bowl

    Homework Statement hi all, why the wave is reflected back form the centre when it is at the distance of 200mm? why the wave can't go beyond 200mm to reach 250mm from the side of bowl? Homework Equations The Attempt at a Solution
  21. L

    Electric flux through a hemisphere

    During my physics lecture, the professor said that flux on a closed surface is equal to zero. What exactly is a closed surface defined as? This problem also requires the use of the Flux = Field * Area formula. In relation to the direction of the electric field, what is the area for Part B...
  22. Saitama

    Oscillation of a solid hemisphere

    Homework Statement I don't have the exact wordings of the problem statement. I hope the following is enough to understand the problem. A solid hemisphere is kept on a plane horizontal frictionless surface. The hemisphere is made to tumble (or toss, I am not sure about the correct word)...
  23. N

    Northern And Southern Hemisphere Of The Unvierse

    I was woundering if the terms "Northern Hemisphere" and "Southern Hemisphere" (of the universe) are used a lot in either an astronomy or astrophysics concepts? Because i have see both those terms being used to describe some ideas for the universe, and i was woundering if anyone could give me...
  24. Z

    Which scatters light more: a sphere or a hemisphere?

    In case the context, which this question is based needs to be provided, the context follows. A sub-project was being done on using sphere or hemisphere "scatterers" on TFSC (Thin-Film Solar Cells). These "scatterers" can be applied on the top of a TFSC in order so that the solar cells can...
  25. C

    Body sliding down an accelerating hemisphere

    We have a frictionless hemisphere M,of a radius R and a body m on the top of it.We give to the hemisphere a horizontal constant acceleration W and consequently the body begins to slide down the accelerating hemisphere.What is the relative velocity of the body in respect to the hemisphere when...
  26. G

    Question about turning a hemisphere into an equivalent circle?

    I was thinking about this when I was trying to work out a simpler way of finding the volume of a sphere. Suppose we cover a hemisphere with a piece of pliable thin cover. Stretching the cover flat would make a circle. The circumference of the sphere is 2*pi*r. The distance along the surface of...
  27. S

    Centre of mass of a solid hemisphere (Feynman way)

    reference to Feyman lectures vol.1 topic 19.2 locating centre of mass Feyman gives us the law of pappus to find the centre of mass ,which he proves for semicircular disc and ring. But when i am trying to extend it to finding the centre of mass of a solid semi-circular solid hemisphere ,i...
  28. N

    Electrical forces between two beads in a hemisphere

    Homework Statement [See image] https://www.physicsforums.com/attachments/61123 Homework Equations Electric force \vec{F}_{e}=k_{e}\frac{q^{2}}{d^{2}}\hat{r} Gravitational force = -mg\hat{j} Normal force = \vec{n} |\vec{n}|cos(θ) = |\vec{F}_{e}| |\vec{n}|sin(θ) = mg ... where θ is the...
  29. M

    How Does Electric Flux Differ Across a Hemispherical Surface?

    Homework Statement A Gaussian surface in the form of a hemisphere of radius R = 6.08 cm lies in a uniform electric field of magnitude E = 9.35 N/C. The surface encloses no net charge. At the (flat) base of the surface, the field is perpendicular to the surface and directed into the surface...
  30. PhizKid

    Field due to a solid hemisphere with uniform charge density

    Homework Statement Given a solid hemisphere with radius R and uniform charge density ##/rho##, find the electric field at the center. Homework Equations ##E = \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{r^{2}}## ##E = \frac{1}{4 \pi \epsilon_{0}} \int \frac{\rho (x',y',z') \hat{r} dx' dy'...
  31. A

    Charge at a distance from a non-conducting hemisphere

    Homework Statement A non-conducting hemisphere of radius R centered at the origin has a total charge Q spread uniformly over its surface. The hemisphere is oriented such that its base is in the (y,z) plane. Find the electric field anywhere along the x-axis for x > 0. Give explicitly the value...
  32. Chronos

    CMB Hemisphere of Evil: Planck Asymmetry Examined

    This paper critically examines the 'hemisphere of evil' CMB asymmetry reported by Planck - CMB Aberration and Doppler Effects as a Source of Hemispherical Asymmetries, http://arxiv.org/abs/1304.3506. Its worth a look if you find this aspect of Planck vaguely disturbing [as I did].
  33. D

    Finding moment of inertia for a hemisphere

    Homework Statement A thin walled hollow sphere of radius 16 cm is sliced in half. What is the moment of inertia of this hollow hemisphere about the x-axis if the areal density is 90 g/cm2? Homework Equations No idea The Attempt at a Solution I've had no luck with this. I've...
  34. Vorde

    Comets in the Northern Hemisphere vs the Southern?

    Hey all, I haven't been alive for that long, so I guess my data probably isn't as good as it should be, but in my experience there have been far more noteworthy comets appearing only to the southern hemisphere, and not to the northern one. In fact, I haven't ever seen a comet (since I was a...
  35. K

    Prove Period of a Rocking Hemisphere of Radius R is Equal to 4R/3

    Homework Statement The hemisphere is of radius R. Prove that the period equals that of a mathematical pendulum of length 4R/3 I have a solution, but i don't understand. Homework Equations Center of gravity: a=\frac{3}{8}R Moment of inertia round the center of mass...
  36. M

    Surface integral and divergence theorem over a hemisphere

    Homework Statement Please evaluate the integral \oint d\vec{A}\cdot\vec{v}, where \vec{v} = 3\vec{r} and S is a hemisphere defined by |\vec{r}| \leqa and z ≥ 0, a) directly by surface integration. b) using the divergence theorem. Homework Equations -Divergence theorem in...
  37. B

    Exoplanet Maps: Northern and Southern Hemisphere Locations

    Exoplanet discoveries continue to be made using various sensitive techniques. Since there is no evidence to the contrary none of them are thought to harbor life forms. Here is a new set of maps showing where the exoplanets are located in both the Northern and Southern Hemispheres...
  38. L

    Solid hemisphere center of mass in spherical coordinates

    Hello, I am struggling with what was supposed to be the simplest calc problem in spherical coordinates. I am trying to fid the center of mass of a solid hemisphere with a constant density, and I get a weird result. First, I compute the mass, then apply the center of mass formula. I divide...
  39. S

    A dielectric hemisphere

    Homework Statement we put a dielectric hemishphere with radius (a) and dielectric coeeficient(k) on an infinite conducting plane.the system(hemsiphere and the plane) are in a constant electric field E0. find the surface charge distrubution on the plane as a function of (r). and explain what...
  40. R

    Finding the Center of Mass for a Hemisphere and Right Cone

    Suppose there's a hemisphere of radius R (say) and a right cone of same radius R but ht. R/2 is scooped out of it then i have to find the center of mass of the remaining part. Here's how i approached... clearly by symmetry, Xcm = 0 Now, Let M be the mass of the hemisphere so...
  41. R

    Center of mass of a solid hemisphere (where's the error)?

    On finding the center of mass of a solid hemisphere i came up with some different result. Here's what i did... consider a small ring at a distance r from the center of the hemisphere and one more ring at a distance of r+dr from center of the ring. let, mass of the small element formed...
  42. O

    Gravitational attraction of a hemisphere at its pole

    Find the gravitational attraction of a solid hemisphere of radius a anddensity1 on a unit point mass placed at its pole. My attempt: Obviously I figured that spherical coordinates would work nicely for this problem. I decided to invert the hemisphere thus placing the pole on the origin...
  43. I

    Circular Motion on a Hemisphere: Finding Speed from Geometric Conditions

    Homework Statement As shown in attached figure, a small object is in uniform circular motion in a horizontal plane, on the smooth of a hemisphere (radius:r). The distance between the object's plane of motion and the hemisphere's lowest point is \frac{r}{5} What is the speed of the object...
  44. H

    Stokes theorem over a hemisphere

    Homework Statement The vector field F is defined in 3-D Cartesian space as F = y(z^2−a^2)i + x(a^2− z^2)j, where i and j are unit vectors in the x and y directions respectively, and a is a real constant. Evaluate the integral  Integral:(∇ ×F)·dS, where S is the open surface of the...
  45. A

    Surface Area of Hollowed Hemisphere - Basic Geometry

    I need to find the total surface area of the hollowed out hemisphere (picture attached), with an inner diameter of 1.86 cm and what looks like an outer radius (also what I am assuming as height) of 1.25 cm. Surface area of a sphere is 4∏r2, so half the sphere is 2∏r2. Since the outer...
  46. B

    Projectile motion on a hemisphere

    Homework Statement A person standing on the top of a hemispherical rock of radius R kicks a ball (initially at rest on the top of the rock) to give it horizontal velocity v_i What must be it's minimum initial speed if the ball is never to hit the rock after it is kicked? Homework...
  47. P

    Surface area of the upper hemisphere

    Homework Statement For upper hemisphere S: x^2 + y^2 + z^2 = 1 , with z≥0, find the area element dS and unit normal vector N. Compute the total area of the hemisphere, ∫∫dS over S. Homework Equations Unit normal to surface f(x,y,z) = const N(hat) = grad(f)/|grad(f)| Surface area...
  48. DryRun

    Evalute surface area of top hemisphere

    Evaluate surface area of top hemisphere Homework Statement http://s1.ipicture.ru/uploads/20120106/jrHc5122.jpg The attempt at a solution This problem is new to me, in the sense that the integration is to be done against S, which is the same region S, over which the limits are defined...
  49. A

    Center of mass of solid hemisphere.

    Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...
  50. A

    Center of mass of solid hemisphere by using angle as variable.

    Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...
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