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.
Homework Statement
You are consulting for an amusement park that wants to build a new "Rotor" ride. In order to increase capacity, they would like to build a unit with a 14.2-ft diameter. The Rotor should provide a centripetal acceleration of 3g. What must be the angular speed in revolutions...
Homework Statement
Find the volume of the solid of revolution when we rotate the area limited by the x-axis and the function f(x) = 1 - cosx where x e [0, 2∏] once around the y-axis?
The Attempt at a Solution
In my notes I have the following equation:
V = ∫ 2∏x f(x) dx
If I put...
Homework Statement
Two double stars of the same mass as the sun rotate about their common center of mass. Their separation is 4 light years. What is their period of revolution?
Homework Equations
Lagranian = T - U = \mu\dot{r}^{2}/2 + \vec{L}^{2}/2\mu r^{2} - Gm_{1}m_{2}/r
F = ma =...
Homework Statement
Problem:
Find the volume of the solid of revolution obtained by rotating the area bounded by the curves y = x^2 – 2 and y = 0 about the line y = -1. Consider only that part above y = -1.
Solution:
The solution is attached as TheSolution.jpeg.
Homework Equations...
Homework Statement
I want the surface area of Revolution about x from [-2,2] of y = |x|
So I want to know if I can take it x from [0,2] and just multiply this result by 2?
Homework Equations
The Attempt at a Solution
Set up
dy/dx = (5/(2√x))
S = 2 ∏ ∫ 5x^1/2(√ 1...
need some help here.
1. find the volume (by washer method) of the solid generated by revolving the region bounded by $y=3+x^2$ and the line $y=4$ about the x-axis.
2. write the integral that will give the volume of the solid generated by revolving the region bounded by $y=e^{2x}$, $x=-1$ and...
Despite the 20+ answers in this thread I think most of us would agree that life for 99% of fantasy world inhabitants would be awful. Strip away the royal courts, the fellowships, the magic schools etc and most of the time you're left with a feudalistic world full of peasants that have to work 10...
Hello MHB,
As students of calculus, we are taught to find the volumes of solids of rotation obtained by revolving given regions about horizontal and vertical axes of rotation. But, what if the axis of rotation is neither horizontal nor vertical? Please consider the following diagram:
We wish...
A solid lies between planes perpendicular to the x-axis at x=-a and x=a for values of a>0 to be given below in parts (i) and (ii). In each case the cross-sections perpendicular to the x-axis between these planes run from the semicircle y=√(a^2-x^2) to the semicircle
y=-√(a^2-x^2).
If...
Homework Statement
Let R be the region between y=tan(x) and the x-axis from x=0 to x=pi/2. Find the volume of the solid formed when R is revolved around the y-axis.Homework Equations
Please try to solve this problem using elementary calculus. The textbook is an elementary calculus textbook...
Homework Statement
A planet of mass ##M## moves around the Sun along an ellipse so that its minimum distance from the Sun is equal to ##r## and the maximum distance is ##R##. Making use of Kepler's laws, find its period of revolution.
(Ans: ##\pi \sqrt{(r+R)^3/(2GM)}##)
Homework...
Homework Statement
Find the volume of solid obtained by rotating the region bounded by y=x^2,y=4 and x=0 about the line x=-2 using the shell method.
Homework Equations
I'm stuck because using disks I got the right answer 136pi/3 but I can't using shells?
The Attempt at a Solution...
Hey guys I'm stuck on this problem. Its an easy one but I need some help..
It's asking for the volume of the solid obtained by rotating the region bounded by y=x^2, y=4, x=0 about the line x= -2 using the shell method.
I got the answer correct using the disk method (answer is 136 pi/3)...
Homework Statement
What multiple of the distance between the centre of the Earth and that of the moon is the distance between the centre of the Earth and a geostationary satellite which above a fixed location on the equator?Take the cycle of revolution to the moon around the Earth to be 27...
Hi, this isn't a specific question but say you had a function y = x - 1 and you were told that the region from x = 1 to x = 3 was rotated 2pi radians and were asked to find the volume of revolution formed.
My question is, would this volume of revolution be the same if they said it was rotated...
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Homework Statement
Find the volume of the solid generated by revolving about the line x=-1, the region bounded by the curves y=-x^2 + 4x - 3, and y=0.
Homework Equations
Shell Method?
The Attempt at a Solution
V= 2pi * ∫x* f(x) dx, where a and b are the lower and upper limits of...
Homework Statement
Find the volume of the solid rotated about the given axis
Homework Equations
∫R^2-r^2dx
Disk method
The Attempt at a Solution
I'm having trouble finding the limits of integration: here's my setup
Pi∫(x^3+1)dx and integrated from -1 to 1. I got this by setting...
A couple of quick questions after watching a video on the helectic model that the solar system follows on it's course around the galactic center. Please bare with me these maybe idiotic questions.
A) Are black holes bound to the spin of the galaxy or do they sit in place on the galactic plane...
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Find the volume of the solid obtained by revolving the region enclosed by y = xe^x , y = 0 and x = 1? - Yahoo! Answers
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How come the area below the graph of \frac 1x between [1, \infty) does not exist, but the solid of revolution below the same graph in that same interval does exist? I do not see the logic.
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Volume of a solid of revolution about x=3? - Yahoo! Answers
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Calculus Disc/washer/shell method.? - Yahoo! Answers
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Homework Statement
The region R shown in Fig. 1 is bounded by the line y=8(x-2), the axes, and the line y=h. Find by integration the volume formed when R is rotated through 360° about the y axis(see Fig. 2)
A whisky glass has the shape indicated in Fig 2 where the units are centimetres...
Homework Statement
In a certain binary-star system, each star has the same mass which is 7.5 times of that of the Sun, and they revolve about their center of mass. The distance between them is the 7.5 times the distance between Earth and the Sun. What is their period of revolution in years...
Calculate the volumes of the rotation bodies which arises when the area D in the xy-plane bounded by x-axis and curve 7x-x^2may rotate around x- respective y-axes.
I will calculate V_x and V_y I start to get crit point x_1=0 and x_2=7
rotate on y-axe:
2\pi\int_a^bf(x)dx
so we get...
Homework Statement
Calculate the volume of the solid of revolution formed by rotating the region around the y-axis. Apply the shell method.
f(x)=e^x, x=0, y=8
Homework Equations
V=∫2∏x((f(x))-g(x))dx
The Attempt at a Solution
This is what I did: (I integrated from 0 to 8)...
Earth is revolving around the Sun at a great speed. Our Galaxy is also moving away from other galaxies at a great speed and so on and so forth there are many kinds of motions that we are subjected to ( Earth's rotation, galaxy's rotation etc.). Plz tell
1. Are all these motions uniform (steady)...
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Calculus ii question!? - Yahoo! Answers
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Homework Statement
Find the volume of 2sin(x) and -sin(x) from 0 to pi revolving around the y-axisThe Attempt at a Solution
My problem is with the geometry of this problem, 2sin(x) is above the x-axis and -sin(x) is below the x-axis. My belief was that I should be adding on the extra area of...
Homework Statement
A torus is formed by revolving the region bounded by the circle x2 + y2 = 1 about the line x = 2. Find the volume of the solid.
The Attempt at a Solution
I've actually got the answer correct. I'm using shell method. My height, h(x), I believe is double the area of...
Homework Statement
Find the volumes of the solids generated
a) x-3y+3= 0, x=0 , y=2 about the x axis
I sketched the graph got a straight line,
I then proceeded to integrate y2
∏∫y2δx
=[(x^3/27)+(x^2/3)+ (x)] from x=3 to x=-3
I got 8∏
but the answer is 5∏
b) x-y2-1=0, x=2...
Homework Statement
Find the volume of the solid generated by rotating about the y-axis
y= 1-x3 x=0 , y=0
I tried sketching the graph of y= 1-x^3 then tried to find the volume from y=1 to y=0.
if x^3 = 1-y
x= (1-y)1/3
so x2= (1-y)2/3
∏∫x2δy
=> ∏∫(1-y)2/3.dy = ∏[ -3/5(1-y)^(5/3)]
I did that...
Homework Statement
Let n>1/2 and consider the function
f(x)=x^{-n} for x\in[1,∞)
Calculate the volume of the solid generated by rorating f(x) about the x-axis, showing all details of your working.
Homework Equations
Since it is rotated about the x-axis, its axis of symmetry is...
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Homework Statement
(a) Consider a binary star system in which the two stars have masses M1 and M2 and the stars move on circular orbits separated by a distance R. Derive the formula for the period of revolution.
(b) Suppose M1= 1.22M and M2= 0.64M (where M = mass of the sun) and R= 0.63...
1. Use the integration capabilities of a graphing utility to approximate the surface area of the solid of revolution. (Round your answer to four decimal places.)
Function:
y = sin(x)
Interval:
[0, pi/4]
revolved about the x-axis
2. Use the area of a surface of revolution...
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Shell method calculus? - Yahoo! Answers
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