Hemisphere Definition and 160 Threads

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. 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...
  2. D

    Finding the Centroid of the surface of a hemisphere

    Hi gang, I was given this question, but I can't quite seem to get it all the way... 1.Determine the coordinates of the centroid of the surface of a hemisphere, the radius of which is r, with respect to its base. Homework Equations A=2\pi r^{2} A: Surface Area of the Hemisphere...
  3. J

    Electric Field in a Hemisphere

    Homework Statement A nonconducting hemispherical cup of inner Radius R has a total charge Q spread uniformly over its inner surface. Find the electric field at the center of curvature. Homework Equations \sigma = \frac{Q}{2piR^{2}} dq = \sigma dA = \sigma R^{2}Sin\thetad\thetad\phi k =...
  4. I

    Center of mass of a hemisphere

    As part of a problem I need to find the center of mass of a hollow hemisphere. I did it in the following way. I considered the lower hemisphere ( around negative z axis ) First by definition, the position vector of the center of mass is obtained as \vec{R}=...
  5. S

    Approximating surface area of hemisphere

    Homework Statement i am trying to apprixmate the surface area of a hemisphere. i am approximating by cutting the sphere into cylinders of different radius, and using their curved surface area to approximate. each cylinder will have a height of r.cos.theta and radius of r.sin.theta...
  6. B

    What is the angle at which a ball falls off a hemisphere?

    Homework Statement A ball with initial velocity 0 and mass m starts at the top of a hemisphere and begins to slid down the frictionless side. The radius of the hemisphere is r. At what angle does the ball fall off the hemisphere?Homework Equations mgsintheta, mgcostheta, fn mv^2/rThe Attempt at...
  7. A

    Hoop stress of a rotating hollow hemisphere

    Homework Statement Hi all! I am an undergraduate who is currently doing a design on amusement ride. MY amusement ride would have a hollow hemisphere that is being rotated by a shaft. I need to determine the stresses acting on the hemisphere in order to know the material to use to build this...
  8. R

    A sphere released from rest from the top of a hemisphere

    EDIT: Problem solved, the mistake was in the statement that the point of contact traces out an arc of length \theta r on the hemisphere. This statement neglects the change in orientation of the sphere relative to the hemisphere. An object with cylindrical symmetry (Full/hollow sphere, cylinder...
  9. B

    How Does a Silvered Hemisphere Affect Image Position in Optics?

    Homework Statement A solid glass sphere of radius R is silvered over one hemisphere. Small object is located a radial distance 2R from the pole of the unsilvered side of the sphere. Find the position of the final image after refraction and reflection. Homework Equations Refraction at...
  10. J

    Find Center of Mass of Hemisphere Homework

    Homework Statement A hemisphere of radius R, covering +/- R in the x and y directions and 0 to R in the Z direction (only the top half of a sphere centered at the origin) Find the center of mass. Homework Equations Cm=(1/m)\int(z dm)The Attempt at a Solution dm is sigma dA, and dA is x dz...
  11. P

    How to calculate dA of a hemisphere.

    I am not sure about how the integrations are initiated at the question below. http://img4.imageshack.us/img4/2831/123io.png Uploaded with ImageShack.us How does dA differ from dV and how are boundaries for integrations are done?
  12. beowulf.geata

    Calculating Area of Hemisphere Cut by Cylinder

    Homework Statement Find the area of the portion of the cylinder x^2 + y^2 = 2x that lies inside the hemisphere x^2 + y^2 + z^2 = 4, z \geq 0. Hint: Project onto the xz-plane. Homework Equations I want to use the formula for surface area \int\int\frac{|\nabla f|}{|\nabla...
  13. K

    At What Angle Does the Object Fall Off the Hemisphere?

    There is a small object, which mass is m on the top of hemisphere, with the mass of M. the size of the object is neglectable. Also, the radius of hemisphere is R. There is no friction between the hemisphere and the object, and the hemisphere and the surface. What if we slightly hit the...
  14. S

    Projecting Area and Flux of Hemisphere, Frustum & Cone

    PREVIOUS POST ----https://www.physicsforums.com/showthread.php?t=165844 THIS POST HELP ME OUT TO SOME EXTENT BUT I AM STILL MESSED UP... I am messed up with the concept of projection of area of different surfaces and flux through different surfaces... Please someone explain it with some...
  15. N

    Surface Integral over a Hemisphere (Work check please I end up with zero)

    Homework Statement Seawater has density 1025 kg/m^3 and flows in a velocity field v=yi+xj, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere x^2+y^2+z^2=9, z≥0Homework Equations Surface integral of F over...
  16. S

    Magnetic Flux through a hemisphere.

    Homework Statement Symbolic question: Consider the hemispherical closed surface in Figure P30.34. The hemisphere is in a uniform magnetic field that makes an angle θ with the vertical. (a) Calculate the magnetic flux through the flat surface (S1), using pi for π, theta for θ, B, and R as...
  17. S

    Minimum Velocity needed to clear a hemisphere

    Homework Statement There is a hemisphere of radius R metres on the ground. You are standing at the very top of the hemisphere and you kick a ball out such that it travels outwards horizontally with speed v metres per second. During the trajectory of the ball, it does not come into contact...
  18. M

    Parallel light rays refraction by glass hemisphere problem

    Homework Statement Parallel light rays travel from air towards a glass hemisphere with radius R and index of refraction ng > nair. A top view is shown in the figure. http://img8.imageshack.us/img8/6380/parallellightrays.jpg (a) Determine where the light rays come to a focus relative to the...
  19. P

    Finding the Angle of Tipping for a Semi-Cylinder on a Ramp

    [/tex]Homework Statement http://emweb.unl.edu/negahban/em223/sexam3/sexam3.htm" number 3...the one about the semicylinder on a ramp Homework Equations \Sigma F_x = 0 \Sigma F_y = 0 \Sigma M=0 f = \mu * N The Attempt at a Solution I got the first part to be 16.7 degrees. However...
  20. S

    Thermal Expansion of a hemisphere

    Homework Statement 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 the summer, when the temperature is 30? Homework...
  21. D

    The current northern hemisphere cold spell

    I have heard a couple of different explations from the jet stream moving south to the alantic dipole shifting. Others are saying that the gulf stream has temporarily shifted towards greenland. Does anyone have a clear idea of what is going on and more important why there has been this shift...
  22. K

    Dynamics - particle moves on smooth inside surface of hemisphere?

    Homework Statement I'm currently working on this question: A particle moves on the smooth inside surface of the hemisphere z = -(a^2 - r^2)^(1/2), r <= a, where (r, theta, z) denote cylindrical polar coordinates, with the z-axis vertically upward. Initially the particle is at z =...
  23. A

    Rate of flow outward through hemisphere

    1. Seawater has density 1025 kg/m3 and flows in a velocity field v=yi+xj, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere x2+y2+z2=9, z≥0 2. surface integral of F over S is ∫∫ F • dS 3. I parameterized...
  24. S

    Surface area of a hemisphere w/ vector calculus

    Homework Statement I need help proving how you could use evaluation of the surface integral \oint\oint f(x,y,z)dS to show that the surface area of the upper hemisphere of radius a is 2\pi a2. So any ideas? Homework Equations The teacher mentioned that the divergence theorem would be...
  25. H

    How Do You Calculate the Charge on Beads in a Hemispherical Bowl?

    Homework Statement "Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconducting walls, the beads move, and at equilibrium they are a distance R apart. Determine the charge on each bead. (Use k_e for ke, g for the...
  26. N

    Sliding on a sliding hemisphere

    Homework Statement A small mass m slides on a hemisphere of mass M and radius R is also free to slide horizontally on a frictionless table. An imaginary vertical line is drawn from the center of the hemisphere to its highest point, where the small mass is originally placed at rest. The angle A...
  27. D

    Physics Physics vacation work in Australia (or the southern hemisphere)

    Hi, I was wondering if anyone could point me to physics labs or really any place to do with physics (not engineering) that take on students in the summer holidays. I am currently in my 2nd year of a B Eng / B Adv. Science degree in Australia. I've looked up places to do with engineering but...
  28. N

    Finding total mass of hemisphere that has a variable density

    Homework Statement Show that total mass of half solid hemisphere radius a given as x^2 + y^2 + z^2 = a^2 and z>=0 and having variable density ρ=1+(r^2)z where r is the distance of any point from the origin is given by: M = (2π(a^3))(6+3(a^3)/18 where M is total mass. Homework Equations -The...
  29. C

    How to Calculate Electric Field at the Center of Curvature of a Hemisphere?

    Homework Statement Charge Q is distributed uniformly over surface of a hemisphere of radius r. Calculate electric field at centre of curvature of hemisphere. Homework Equations I realize that this should be quite straightforward but I am a bit confused. The total charge Q is...
  30. L

    Finding Centre of Hemisphere - Radius a

    imagine a hemisphere of radius a with the circle lying in the x-y plane and so the axis of the hemisphere is the z axis. if z=0 is at the centre of our circle, what value of z corresponds to the centre of the hemisphere? i used z=a/2 but have a sneaky feeling its' meant to be...
  31. pellman

    How does a hemisphere differ from a disk?

    Can the surface of a hemisphere be distinguished from a disk without introducing a metric? What is the minimum amount of info we need to know to identify one space as a disk and the other as the surface of hemisphere? Both can have the same coordinate chart. For example, distance from...
  32. A

    Electric field at the center of curvature of a solid hemisphere

    Homework Statement Hi, I'm wondering if this is the proper way to approach this problem. The question says to: a)find the electric field at the center of curvature of the hemisphere (center of the flat bottom). Homework Equations Gauss's law: integral E*da = Qencl/epsilon...
  33. B

    Hemisphere being pulled by a rope problem

    Homework Statement A hemisphere of radius R and mass M, curved side down, is pulled along a plane at a constant velocity by means of a horizontal force F. The coefficient of sliding friction is mu. Find the the angle at which the hemisphere is inclined as it is pulled. C.M. of the...
  34. G

    Centre of mass of a solid hemisphere.

    Hi there, I can't get my head round how to do the math for this problem. I'm sure it's not as hard as I think... Homework Statement Show that the CoM of a uniform solid hemisphere of radius r lies at a distance (3/8)r from the centre of the flat face. You may find it convenient to regard the...
  35. M

    [Calc 3] Gauss' Law for Elecricity over a hemisphere

    Hello, Thank you very much for takign the time to help me out. This is an applied calculus 3 (multivariable calc) level problem. I have an answer, but it is nonsensical as the units are not in accordance with units of charge, C. Homework Statement Instructions: Use Gauss' Law for...
  36. J

    Divergence theorem over a hemisphere

    I was told this problem could be done with divergence theorem, instead of as a surface integral, by adding the unit disc on the bottom, doing the calculation, then subtracting it again. Homework Statement Homework Equations The Attempt at a Solution for del . f I get i + j =...
  37. G

    Why at the south hemisphere the sun rises from the west?

    Hello I wanted to ask why at the south hemisphere the sun rises from the west? We know that Earth rotates reversely than the watch pointers(this happeness to both hemispheres),so all the "sky" (the stars etc..) goes to the opposite direction. If someone could explain me.. Thank you!
  38. H

    Moment of Inertia of a Hemisphere

    Homework Statement The moment of inertia of a uniform sphere of mass m and radius r about an axis passing through its center of mass is (2/5) mr^2. If half of the sphere is removed, what is the moment of inertia about the same axis? Homework Equations integral of r^2 dm The Attempt at a...
  39. G

    Determine the x-coordinate of the mass center of the homogeneous hemisphere

    Homework Statement Determine the x-coordinate of the mass center of the homogeneous hemisphere with the smaller hemispherical portion removed? I know what the answer should be it's Xcm = 45/112 R Homework Equations The center of mass R of a system of particles is defined as the average...
  40. R

    Finding the Center of Mass of a Hemisphere

    Homework Statement Center of Mass of a hemisphere http://www.goiit.com/templates/default/images/chapters/center_mass/image064.gif http://www.goiit.com/templates/default/images/chapters/center_mass/image068.gif Why is volume of elemental disc = Rd\theta (cos \theta) (\pi R^{2}cos^{2}...
  41. P

    Solved: Solving Ball Kicked from Top of Hemisphere Problem

    Homework Statement A person standing at 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 Vi. What must be its minimum initial speed if the ball is never to hit the rock after it is kicked? With this initial...
  42. H

    Work done in a Gravitational Feild of a Hemisphere

    The problem concerns with the work done by the Gravitational Feild force exerted on a mass 'm' kept on the center of the base of a hemisphere of mass "M" radius "R". The way I did it was, first I found the Center of Mass of the hemisphere which is 3R/8. Next I used the concept => Work done=...
  43. T

    Stargazing 101: Adjusting for Hemisphere

    Where to look? When I see a news story about when to see celestial events (in this case an alignment) how much to I have to adjust for my geographic position on the Earth?? I am reading a story directed at those in the United States, but as I am currently in a different hemisphere how would I...
  44. Holocene

    Northern Hemisphere: Impact on Global Population & Maps

    I'm not much of a historian, but I believe that if you take a good look at history, most initial technological advances, understandings in science, formation of governments, religions, most everything we associate with the so-called "modern day world", including civilizations themselves, have...
  45. M

    At what height does the boy lose contact with the ice?

    Homework Statement "A boy is initially seated on the top of a hemispherical ice mound of radius R = 13.8m. He begins to slide down the ice, with a negligible initial speed. Approximate the ice as being frictionless. At what height does the boy loose contact with the ice?" Homework...
  46. Holocene

    How much snow does the southern hemisphere see?

    Does it snow in places like southern south America or southern Africa durring their winter seasons? If not, why?
  47. X

    Electric Flux through a hemisphere

    Homework Statement "What is the flux through the hemispherical open surface of radius R? The uniform field has magnitude E. Hint: Don't use a messy integral!" \mid \vec{E} \mid= E radius = R Homework Equations Electric Flux over a surface (in general) \Phi = \int \vec{E} \cdot \,dA...
  48. P

    Continents on the northern hemisphere

    I am supprised and puzzled when my nephew, a 14 year old boy asked me : 'Why most of the continents are on the Northern hemisphere ?'. I answered him it is just a coincidence. Could anybody explain if there are any real reasons for that? Thanks
  49. C

    How Do You Calculate the Velocity of a Ball Orbiting Inside a Hemisphere?

    How would i calculate an equation for the velocity of a ball inside a hemisphere ( the ball is orbiting in a horizontal circle inside the hemisphere)
  50. Q

    Radius probability of random cut hemisphere.

    Imagine viewing a hemisphere normal to the equator such that it looks like a circile with the full radius of the hemisphere. Now randomly section or cut the hemisphere in a manner a tomato is sliced. If we only consider the portion of the hemisphere that contains the pole we should be...
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