What is Revolution: Definition and 410 Discussions

In political science, a revolution (Latin: revolutio, "a turn around") is a fundamental and relatively sudden change in political power and political organization which occurs when the population revolts against the government, typically due to perceived oppression (political, social, economic) or political incompetence. In book V of the Politics, the Ancient Greek philosopher Aristotle (384–322 BC) described two types of political revolution:

Complete change from one constitution to another
Modification of an existing constitution.Revolutions have occurred through human history and vary widely in terms of methods, duration and motivating ideology. Their results include major changes in culture, economy and socio-political institutions, usually in response to perceived overwhelming autocracy or plutocracy.
Scholarly debates about what does and does not constitute a revolution center on several issues. Early studies of revolutions primarily analyzed events in European history from a psychological perspective, but more modern examinations include global events and incorporate perspectives from several social sciences, including sociology and political science. Several generations of scholarly thought on revolutions have generated many competing theories and contributed much to the current understanding of this complex phenomenon.
Notable revolutions in recent centuries include the creation of the United States through the American Revolutionary War (1775–1783), the French Revolution (1789–1799), the Spanish American wars of independence (1808–1826), the European Revolutions of 1848, the Russian Revolution in 1917, the Chinese Revolution of the 1940s, the Cuban Revolution in 1959, the Iranian Revolution in 1979, and the European Revolutions of 1989.

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  1. M

    Areas of surfaces of revolution

    Hello. I just started to study integral calculus not long ago and I have some confusion when it comes to calculating the areas of surfaces of revolution using integral. As from my testbook, when we want to calculate this kind of surface area, we often use the frustum surface area to approximate...
  2. J

    Do you expect that there will ever be another massive revolution in physics?

    We've had some major theoretical developments in physics in the past - Newton, Einstein etc. immediately spring to mind - but it seems to me that we haven't really had a new way of thinking or a new branch of physics being born in a long time. Do you think there will ever be another person who...
  3. P

    How do you find the volume of a solid of revolution using integration?

    Homework Statement x=2y^2 x=0 y=+-6 rotated around y Homework Equations integral 2pi*x(f(x)dxThe Attempt at a Solution integral from -6 to 6 of 2pi*y*2y^2 dy but i get something far less than the correct answer
  4. C

    Easy solids of revolution clarification

    Homework Statement Calculate the volume of the solid of revolution formed when you rotate region R, delimited by f(x) = x^2 from x = 0 to x = 3, around: a)the x axis b) the y axis The Attempt at a Solution I solved it using the disc method. a) dV = pi * x^4 * dx. thus V = (pi*...
  5. U

    Calc2: Solid of revolution about y=2 question

    Hi All, I had a question about this problem I was doing and was hoping to see if I did it right. Homework Statement Using Disk or Washer method Find volume of the solid generated by revolving the region bounded by y=sqrt(x), y=2, x=0 about the line y=2.Homework Equations Disk Method...
  6. V

    Volume of Solid Revolution

    Hi all. I've just hit a block in the following question: [Find the volume of the solid...] "The region in the first quadrant bounded by the curve y = x^2, below by the x-axis, and on the right by the line x = 1, revolved around the axis x = -1." I've tried nearly 2 hours figuring the...
  7. R

    Volume of Revolution for Polynomial Bowl

    Homework Statement The question asked is to make a bowl out of polynomial equations rotated around the y axis. The bottom of the bowl has to have a maximum at the center and a minimum at some distance from the center. The equations I want to use are x^2+10, 1.3x^2 and -.7x^2 + 4. The...
  8. R

    Volume of Solid of Revolution Question

    Homework Statement y= -(x/6) + b, find the volume as this solid is rotated 360 degrees around the Y axis Homework Equations If I were given the interval at which I needed to find the volume and/or the value of B I could easily do this using the formula: [pi] Integrate: (R(y))2 dx...
  9. E

    How can we use calculus to find volumes of revolution?

    As part of an assignment on Approximating Areas and Volume I am asked to derive the equation shown in the image attached. The question reads: "It can be shown that if y = f(x) is revolved around the x-axis to form a solid between x=a and x=b then the volume of the solid is give by the...
  10. P

    Solid of revolution (should be simple)

    Hey. Thanks in advanced for the help. This site has helped me a lot through the years. Homework Statement Find the volume of the solid formed by rotating the area within y=e^x and y=sin x when 0<x<pi Homework Equations The Attempt at a Solution I've tried it like 10 times on...
  11. I

    Finding surface of revolution

    Homework Statement Find the area of the surface of revolution generated by revolving about the x-axis the cardioid x=2cos\vartheta-cos2\vartheta,y=2sin\vartheta-sin2\vartheta. pictures show a cardioid with \vartheta=pi and \vartheta=0. Homework Equations After looking up, the formula...
  12. K

    Max & Min Frequencies from Tuning Fork Revolution

    Homework Statement A tunning fork with frequency f = 512 Hz is held by someone who swings it vigurously in a circle in the horizontal plane. The radius of the circle is 1.0 m, and the frequency of revolution is 3.0 rev/s. (a) What are the max and the min frequencies that a second person...
  13. O

    Volume of Solids of Revolution

    Homework Statement In Problems 1-5, let R be the region bounded by y√x =, y = 1, and x = 4. Each problem will describe a solid generated by rotating R about an axis. Write an integral expression that can be used to find the volume of the solid (do not evaluate). I only need help with problem...
  14. N

    Solving Bacterial Motor Angular Speed and Time for One Revolution

    Homework Statement Some bacteria are propelled by motors that spin hair-like flagella. A typical bacterial motor turning at a constant angular velocity has a radius of 1.8x10-8m, and a tangential speed at the rim of 1.8x10-5 m/s. (a) What is the angular speed (the magnitude of the angular...
  15. J

    Solids of revolution - What if the axis crosses the volume?

    Homework Statement Here is the problem : Find the volume of the solid generated when the area bounded between the following functions rotates along the y=4 line. Functions: y=x^3 y=4x Homework Equations Functions...
  16. S

    Volume of Revolution: Find the Volume from y = x+6 & y = x^2 - 4x

    Homework Statement The line y = x + 6 meets the curve y = x2-4x at the points P and Q. Find the volume of the solid generated when the area enclosed by the line and the curve is rotated through 360o about the x-axis Homework Equations Integration The Attempt at a Solution I've...
  17. N

    Central Force (period of revolution and period of small radial oscillations)

    [b]1. A particle of mass m and angular moment L moves in a central force V=(1/2)kr^2 (k>0). Find the period of revolution for the circular movement and the period of small radial oscillations around the stable cicular orbit. Homework Equations The Attempt at a Solution Well I tried...
  18. Jonnyb42

    Weight Measurement on Mutually Orbiting Planets

    So at the end of the lengthy thread https://www.physicsforums.com/showthread.php?t=404650", a similar but new question of mine arose: If you consider the Earth rotating, you can measure differences in weight at different points on the Earth (namely, the extremes being the poles and the...
  19. A

    Volume of Revolution: Cylinders vs Washers

    Homework Statement Find the volume of the solid bounded by the curves y = x^{1/3} and y = x when rotated around y=1. Homework Equations Volume with washers: V = \pi \int R(x)^{2}-r(x)^{2} dx where R(x) and r(x) are functions of x defining the inner and outer radii of the washers...
  20. F

    Solids of Revolution, the negatives don't matter right?

    Homework Statement Use the method of cylindrical shells to nd the volume of the solid obtained by rotating the region bounded by the curves y = x4, y = 1, x = 0 about the y-axis. Sketch the region and a typical shell The Attempt at a Solution I am just going to set it up, but I am not going...
  21. A

    How Does Translating a Region Affect the Volume of a Solid of Revolution?

    Homework Statement Find the area of the region bounded by y=0, x=9, y=x/3 and rotated about y=-2 The Attempt at a Solution The answer is \pi\int^{9}_{0}(2+x/3)-2^2dx I'm just wondering if this is the same thing as saying find the area of the region bounded by y=2 instead of y=0...
  22. K

    Surface Area of a Solid of Revolution

    Homework Statement Find the area of the surface generated when you rotate the parabola y=x2 0 less than or equal to x less than or equal to the square root of k, around the y-axis. You should end up with a simple formula in terms of the constant k. Homework Equations S=2\pi\intyds...
  23. B

    Finding Surface Area of a Solid of Revolution

    Homework Statement Find the surface area generated by rotating y=5-4x^(3/2), 0\leq x\leq 1 about x=2.Homework Equations SA = 2\pi\int_{a}^{b}(r\cdot ds)dx The Attempt at a Solution I simply filled in the formula for the given question, and I'm getting stuck at integration time. SA =...
  24. 0

    Volume of revolution. Could someone check this please?

    Homework Statement The region bounded by y=e^{-x^{2}}, y=0, x=0, and x=1 is revolved about the y-axis. Find the volume of the resulting solid. Homework Equations integral from a to b of pi*f(y)^2The Attempt at a Solution If y=e^-x^2 and I am revolving about the y-axis then I need to rewrite...
  25. S

    MATLAB MATLAB: Plotting help, turning 2D plot into 3D volume of revolution

    Hi I have an issue I am trying to solve, so far I haven't managed to get past it. I have some data for 200 points in theta from 0 to 2PI. The data is spherically symmetric so there is no phi dependence. Basically what I want to do is turn the 2D plot into a 3D by revolving the 2D plot. My...
  26. S

    2nd semester calc question : calculating volume of solid of revolution

    Homework Statement The solid formed when the region bounded by y = x^2 and y = 2 - x^2 is revolved about the x-axis Homework Equations disc method with respect to x-axis the integral of : (pi * (f(x)^2 - g(x)^2)) The Attempt at a Solution When I square each function and...
  27. S

    Surface area of solid of revolution with undefined derivative

    Hello there. Suppose I have a function: y=3x^{2/3}-1 I want to find the surface area of the solid formed when the part of the curve between x=0 and x=8 is revolved about the x-axis.The curve crosses the x-axis at a point (1/3)^{3/2} The derivative of the function is...
  28. P

    Volume created by the revolution of a polar function around the initial line

    Hello, I was wondering if anyone could help me with deriving the volume created by the rotation of a polar equation around the initial line. So, I thought about adding the surface area of cones (multiplied by d\theta) if each cone the triangle created with s-length of f(\theta) and r-length...
  29. A

    Single Var Calculus - Volumes of Revolution

    Single Var Calculus -- Volumes of Revolution consider the curves y = 6 x = 0 and y = x2+2 Revolve the bound area around the y-axis and find the volume of the product solid. Here's what I did. r = x = (y - 2)1/2 V = pi * INTEGRAL from y = 2 -> y = 6 of r2 dy = y - 2 dy = y2/2 -...
  30. P

    Determining revolution using Angular Motion

    Homework Statement The combination of an applied force and a friction force produces a constant total torque of 35.0 N · m on a wheel rotating about a fixed axis. The applied force acts for 5.90 s. During this time, the angular speed of the wheel increases from 0 to 10.1 rad/s. The applied...
  31. T

    Volume of Revolution Problem: Calculating the Total Volume of a Haystack

    Homework Statement The height of an (axially symmetric) pipe z as a function of the distance from the axis of symmetry is z = 2-2x^{2} , where both z and x are measured in metres, and where 0 \leq z \leq 2 and 0 \leq  x  \leq 1 What is the total volume of hay in cubic metres in...
  32. A

    Volume of Revolution: Find Vol. Bounded by y=6-2x-x2, y=x+6 About x=1

    Homework Statement Find the volume of the solid generated by revolving the region bounded by the given graph about the indicated line using any method. y=6-2x-x2 y=x+6 About the axis x=1 Homework Equations Shell method: 2*pi * INT[ p(x) * h(x) ] dx The Attempt at a...
  33. M

    Area of Surface of Revolution of ln(sec x) 0< x <(pi/6) W/A is no help here

    I tried doing just the integration and I was totally stumped, and Wolfram-Alpha has been no help at all Find the surface area obtained by rotating about the x-axis: ln(sec x) for 0 < x < (pi/6) This problem appeared on an exam I had, but all that was required was to set up the...
  34. I

    Calculating distance travelled per revolution

    Hi, A cylinder is to be coated on a rotating lathe, with a coating rod moving by a mechanical robot in the X direction (back and forth). The cylinder is 300mm in length, 19mm in diameter. What is the distance traversed per revolution of a rotating cylinder, with the lathe rotating at 1200RPM...
  35. TrickyDicky

    Dark matter and keplerian revolution

    Dark matter is believed to have a more homogenous distribution than normal matter, a bias of at least 2 is used in models of large-scale structure in order to justify large voids and superclusters in a homogenous universe. If Dark matter is so evenly distributed I have some difficulties to...
  36. M

    Solid of revolution question: verify that the volume of the cone is παβh/3

    Homework Statement Consider a vertical cone of height h whose horizontal cross-section is an ellipse and whose base is the ellipse with major and minor semi-axes α and β. Verify that the volume of the cone is παβh/3. [ Hint: The area of an ellipse with major and minor semi-axes α and β is...
  37. S

    Finding volume of axis of revolution

    Homework Statement 2\pi \int_0^6 y\sqrt{25- (y- 1)^2}dy + 5\pi That's the integral i need solved 2. The attempt at a solution[/b] so first i subbed u=y-1 took the 2 pi out of the integral that got me 2 integrals u*sqrt(25-(u)^2) du + sqrt(25-(u)^2) du the first integral =...
  38. S

    Finding volumes by rotating around an axis of revolution

    1. Homework Statement k so here is the equation i need help with that will find me the volume of a sphere 2*pi*y*sqrt(25-(y-1)^2) dy - 5*pi from 0 to 6 the 5 pi is the volume of a cylinder 2. Steps so first i subbed u=y-1 took the 2 pi out of the integral that got me 2 integrals...
  39. J

    Multiple Rotating Masses in Revolution

    I've simplified my question to make it easier to explain; I'm trying to find a way to determine the motion of a freely turning body as resultant of 2 counter-weights on rotating arms. Here's my write-up: Description: Electric motors turn both orange shafts clockwise at constant angular...
  40. S

    Volume of a solid of revolution

    Can anyone confirm if I have done the following work correctly Find the volume of a solid of revolution obtained by rotating about the y-axis the region bounded by y = the fifth root of x and 2x^2 - 3x + 2. By drawing the graph, I figured out that I need to use the method of cylindrcal...
  41. Telemachus

    Solving Solids of Revolution: Cylinder vs Function of Y

    Homework Statement Hi, well, I don't have to solve any problem yet. I have an inquietude about solids of revolution. I've been reading this: http://en.wikipedia.org/wiki/Solid_of_revolution and this: http://en.wikipedia.org/wiki/Disk_integration What I wanted to know is if its the same this...
  42. E

    Volume of Solids of Revolution

    Find the volume of the solid st, 1. y=cos x , y= 0 in [0,pi] ; Rotated around x=1 2. I am slightly confused, I see that the area will double around twice so I can just use the left half of the curve. I am just not sure how to do so.
  43. S

    Exact Volume of Solid of Revolution for y=cos(x^2) | Rotating about x and y-Axis

    Homework Statement let R be the region enclosed by the x-axis,y-axis and the curve y=cos(x^2) A)find the exact volume of the solid of revolution obtained by rotating R about the y-axis B) find the exact volume of the solid of revolution obtained by rotating R about the x-axis i am lost on the...
  44. F

    Volumes of Solid of Revolution

    I have a volume problem that I has been bothering me for a while now, as I have just not been able to figure it out. The question involves finding the volume of the solid generated by revolving the region bounded by y = x, y = 0, and y = 4 around the line x = 6. I tried doing \int ^{4}_{0}16...
  45. L

    Solve Volume of Revolution Problems: Tutorial & Examples

    Homework Statement I'm having a bit of trouble when it comes to volume of revolutions and areas. I find it quite difficult when it comes to setting up the integral. I'm not sure when to use the shell or washer method. Could someone explain to me or give me a tutorial on how to set up the...
  46. L

    Volume of revolution and areas

    I'm having a bit of trouble when it comes to volume of revolutions and areas. I find it quite difficult when it comes to setting up the integral. Could someone explain to me or give me a tutorial on how to set up the equations thanks! Here are a few examples The region enclosed by the...
  47. W

    Revolution of earth around sun

    I got into an argument with someone over Earth revolving around the sun vs sun revolving around the earth. He stated that there are reference points within the universe where the sun appears to revolve around the Earth that are NOT on the surface of the earth. I conceded that perhaps a point...
  48. K

    Volumes of solids of revolution

    Homework Statement A circle with a radius of (a/2) is bored through the centre of a sphere of radius a. Find the volume of the remaining solid. Homework Equations The Attempt at a Solution I've been trying this for an hour now and I've been trying to find the remaining volume by...
  49. James889

    Calculating Area of Solids of Revolution

    Hi, I have the area D(x,y): \sqrt{x}e^{x^2}\leq y \leq 3,~~ 0\leq x \leq 1 That is rotated about the x axis, and i need to calculate the area \pi \int_0^1 3^2-y^2 = \pi \int_0^1 9-xe^{2x^2} \frac{-9\pi}{4}\cdot (e^{2x^2}-1)\bigg|_0^1 But this is all wrong, why?
  50. James889

    Solids of revolution, y axis

    Hi, The area e^x-1 Is rotated about the y axis, bounded by y=1, x=0 and x=ln2 find the volume of the solid. And i am clearly making something wrong, so if anyone could verify my work. ~ 2\pi\int_0^{ln2}x\cdot(1-(e^x-1) -2\pi\int_0^{ln2}xe^x-2x Integration: u=x, du=1 dv=e^x, v=e^x...
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