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.
Is it possible to revolve a function around y = x? If so how would you do it?
I suppose the main difficulty is in finding the radius for the area of a disk or cylinder. Is there any method that works will all or most functions?
Homework Statement
Volume of the region bounded by y = x^2 and x = y^2 about y = 1
Homework Equations
\pi r^2
The Attempt at a Solution
So the functions look something like this:
I decided to use method of washers with respect to x.
The radius if the center is at y = 1 of...
Homework Statement
A toy truck moves around the outside of a circle of radius 0.6m at 2 revolutions per second
Calculate:
a: the angular speed of the truck
b: the linear speed of the truck
c: the period of revolutionHomework Equations
ω= \frac{2π}{T} \\
v=rω
??
The Attempt at a Solution
For...
Suppose I have a region R whose boundary extremely complicated. While it would take me hundreds of years to approximate the boundary with formulae, I can easily estimate the area of R within a desired precision. I want to find the volume of the solid of revolution of R .
My intuition told...
Here is the question:
Here is a link to the original question:
Find the volume V of the solid obtained by rotating the region bounded by x=16-(y-3)^2, x+y=7 about the x-axis? - Yahoo! Answers
I have posted a link there to this topic so the OP can find my response.
First, let's take a look...
Homework Statement
From K&K's 'Intro to Mechanics'
Find the shortest possible period of revolution of two identical gravitating solid spheres which are in circular orbit in free space about a point midway between them.
Homework Equations
The Attempt at a Solution
So I figured...
Homework Statement
Planet A (at X meters) completes 1 full rotation (Y sec). Planet A then shrinks to (X2 meters)
What is its rotation speed now.
Conservation of angular momentum
Homework Equations
T=2pi/w
W=V/r
The Attempt at a Solution
I found how to reverse engineer the...
I have a question about the concepts of rotation and revolution - on how they are treated in relativity.
Since all motion is relative, a revolution of a planetary body around a central body could also be seen instead as a rotation of the central body w.r.t. a fixed (non-revolving) planetary...
Good morning everyone! I have been presented the following problem:
Find the volume of the revolution solid around the $x$ axis of the region between the curves $y=x^2 +1$ and $y=-x^2 +2x +5$ for $0 \leq x \leq 3$.
Finding the intersection of the curves yields $x=-1$ and $x=2$. Therefore, I...
Hi,
I have a question concerning solid of revolution.
The bowl-shaped volume formed by rotating the area circumscribed between y=bcosh(1) and y=bcosh(x/a) around the y-axis was given to us by the instructor as pi*b*int [x^2*d(cosh(x/a))] between 0 and a.
My question is why are the integration...
Homework Statement
Consider the region of the x y plane given by the inequality:
x^2 + 4x + y^2 - 4x - 8 ≤ 0;
If this region rotates an angle of π/6 radians around the line given by the equation x + y = 0, it will create a solid of revolution with surface area equal to
(i)...
In my calculus exam, I would like to know for all of the questions that I am 100% right (who wouldn't?). I can be sure of this for most basic questions using my graphics calculator (fx-9750gii) and some simple maths. One thing I want to know how to be "completely sure" to solve are solid of...
Greeting everyone I am trying in integrate this function, to obtain the surface of revolution of a function.
1. Relevant equations
\int_{-1}^{1} 2\pi\sqrt\frac{x^2 (1 - x^2)}{8}\sqrt{1+(\left| x\right | \frac{-2x^2+1}{2(-x^2+1)^{1/2}*2^{1/2}x}})^2
2. The attempt at a solution
I tried to...
Homework Statement
Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified line. Sketch the
region, the solid, and a typical disk or washer.
y=sinx, y=cosx, 0≤ x≤∏/4, About y=-1Homework Equations
The Attempt at a Solution
Tried 2 ways, shell...
"Revolution" TV show
Less than 3 weeks to the premiere now. (September 17). What do you think? Will it be it be silly but fun to watch like Flash Forward, or awful like Flash Gordon?
I would love to hear a technobabble explanation for this, but I don't think we'll get one.
The show is...
Let f(x)=9-x^2. Let A be the area enclosed by the graph y=f(x) and the region y>=0.
Suppose A is rotated around the vertical line x=7 to form a solid revolution S.
So, using the shell method, I was able to find the indefinite integral used.
I found the shell radius to be (7-x) and the shell...
Homework Statement
Find the area of the surface obtained by rotating the curve y=x3, 0≤x≤2 about the x-axis.
Homework Equations
\begin{equation*}
SA = \int_{0}^{2} 2 \pi y L
\end{equation*}
The Attempt at a Solution
SORRY, I don't know how to use LaTeX yet.
∫2∏y√(1+(dy/dx)2)dx from 0->2...
Tell me if this is a fair characterization of the first superstring revolution or the discovery made by Schwarz-Green in 1984. Schwarz-Green found a theory that allowed for the cancellation of anomalies provided that 10 dimensions existed and the gauge group is (SO(32) and E8 x E8) which...
Homework Statement
For an assignment, I'm required to design three water bottle using 3 different polynomial functions. I've used a linear, quadratic and cubic. The first bottle needs to be 600ml, the second 300ml, and the third 1L.
In order to 'create' the bottles, we are to calculate the...
Apparently when a "snifter" glass is placed on it's side and filled up to the tip, this volume is the optimum amount that should be poured to make a shot.
Hence i have put a glass on an axis and modeled an equation for the top half of the glass...
f(x)=...
Assume that the implicit equation of the one-sheeted hyperboloid is
(x/a)^2 + (y/a)^2 - (z/c)^2 = 1
How am I able to obtain the surface area of hyperboloid ?
Thanks
Homework Statement
Having recently learned the disk/shell/washer method for finding the volume of a solid of revolution, I'm trying to apply similar methods to derive the formula for the surface area of a cone (and hopefully after that, that of a sphere).
The region that is revolved around...
Homework Statement
Find the volume of the area bounded by
y^2 = 4ax
and
x=a
rotated around the x-axis.
Homework Equations
integral of pi R^2 dh
The Attempt at a Solution
I just don't know how to handle the x=a part of the boundary. Any hints? thanks
Hi everyone! I have two questions, one about area of surface of revolution and another is about arc length...
I really fail to do this two question despite many times of trying so I hope someone can help me
1. Find the area of the surface of revolution generated by revolving the arc of the...
Hi dudes,
My questions are:
What does planet's revolution depends?
If for example is there a planet 4 time the mass of the Earth at about its same distance from a star 4 time the mass of sun, could it be it has the same revolution period ot the eath?
I'm finding myself stuck again. This time it is more in the set up then the solving.
Find the volume of the following solid of revolution.
The region bounded by y=\frac{1}{x^2}, y=0, x=2, x=8, and revolved about the y-axis.
I am trying to use the shell method to solve this, as it seems the...
Hey guys and gals. Hoping someone can help out with a problem I am finding myself stuck on.
The question goes as follows.
Solids of revolution. Find the volume of the solid of revolution. The region bounded by \(y= \frac{ln(x)}{\sqrt(x)}\), y=0 and x=2, revolved about the x-axis.
The problem...
It's not a popular series, but there's a lot of sci-fi talk in there that's really interesting (mostly related to space/planets/stars). Lol just wondering if anyone has read it
Homework Statement
Find the area of the surface generated by revolving the curve
Homework Equations
x = 5(cos3t), y = 5(sin3t), 0 ≤ t ≤ \pi, about the y axis.
The Attempt at a Solution
x' = -15(cos2t)(sin t)
y' = 15(sin2t)(cos t)
(I think this forms the top part of an astroid)...
What single invention between 1775 and 1913 has had the biggest impact on humanity and why? Also it could be a process like say the Bessemer process or a simple item like the lightbulb.
For anyone who hasn't seen it yet, did google get you with this?
Gmail Tap
Google typically does some pretty clever things for April Fools, and I typically see right through. This one got me though, I thought to myself, "Oh great now I'll have to learn Morse Code."
I was actually stupid...
Hi,
I am doing a project for the math department and in it I would like to revolve this piecewise (3) function about the x axis. I have found programs like winplot which are pretty easy but it will only show the finished product. I am looking for something that I can either manipulate or it...
Homework Statement
Here is the surface I need to parameterize. It is a solid of revolution.
Homework Equations
The Attempt at a Solution
So since its a piecewise function, I can define it as follows
(x-2)^2 + z^2 = 1, 1<x<2
z = -x+3, 2<x<3
z = x-3, 2<x<3
I know...
Homework Statement
Find the volume of a solid created when the area between the function y=x^2+1 and the x-axis (for 0<x<2) is rotated about the line y=-2.
Homework Equations
Vs = ∏*r^2*h
The Attempt at a Solution
I can't seem to set this up correctly and am thrown by the inner radius...
Finding period of revolution of an electron (fairly urgent)?
Homework Statement
A doubly ionized atom (charge = +2e) whose mass is 3.65E-26 kg is accelerated by a voltage of 3950.0 V and enters a region where a uniform magnetic field B = 0.0500 T acts perpendicular to its motion.
a) What is...
Homework Statement
Find the volume of the first quadrant region bounded by x=y-y3, x=1 and y=1 that is revolved about the line x=1.
The Attempt at a Solution
dV=∏R2t
where :
t=dy
R=1-(y-y3)
=1-y+y3
so..
dV=∏(1-y+y3)2dy
dV=∏(1-2y+y2+2y3-2y4+y6)dy
V=∏∫ from 0 to 1 of...
Homework Statement
A cylinder is initially at rest, how long will it take for the cylinder to turn one revolution?
Homework Equations
(Theta)f=(Theta)i+(alpha)(deltaT)
The Attempt at a Solution
I know that the distance of the cylinder to turn one revolution is 2Pi over speed. My...
Homework Statement
Find surface area of solid of revolution obtained by rotating the curve:
y=x2/40-5lnx
from x=5 to x=7, rotated about x=-4
The Attempt at a Solution
The problem is I know how to do this if I rotated it about x-axis/y-axis, but I have no idea how to do it if the...
I am currently learning about volumes of revolution in calulus, and have looked ahead to surfaces of revolution as well. I want to try and extend this concept to revolving 3d functions over the x-axis into the fourth dimension. I found this thread...
Homework Statement
A cathedral dome is designed with three semi circular supports of radius r so that each horiontal cross section is a regular hexagon. Show that the volume of the dome is r^3 * sqrt(3)
an accompanying figure - http://imgur.com/3fSqh
Homework Equations...
Homework Statement
Find the volume of the solid obtained by rotating the region bounded by y=2x2-x3 and y=0 about the y-axis
Homework Equations
There no required method (between Disk, Washer, Shell). In my attempt below, I used the Shell method, I believe. 2π(shell radius)(shell...
Homework Statement
Hey we have started solids of revolutions using disk, washer, and shell methods. But I came across a problem i cannot figure out. "The region of the graph of y=x^2 and the x-axis, for 0<x<2, rotated about the line y=4.
Homework Equations
Area of a circle = ∏r^2...
planets do not loose energy when they orbit the sun due to interplay of centripetal and centrifugal force. Then why is this system not able to explain that electrons do not loose energy while orbiting the nucleus?
I have to find the volume of the solid whose area is bound by the equations y=-x+3 \ and \ y=x^2-3x as it revolves around the x and y axis. I approached it by finding the center of mass and then using Pappus's theorem:
M_{x}=\int^{3}_{-1} \frac{1}{2}((-x+3)^2-(x^2-3x)^2)\,dx = \frac{64}{15}...
I'm surprised this hasn't been discussed yet. Apple not too long ago announced their intent to enter the world of textbooks. This capability was likely at the forefront of the decision to develop the iPad.
The upside is that the textbooks can be easily updated, dynamic and mobile. The...
can Earth revolve around the sun without rotating itself? why some planets revolve clockwise and some other anticlockwise? what decides this direction?
Homework Statement
Find the volume obtained by rotating the solid about the specified line.
y=2-(1/2)x, y=0, x=1, x=2, about the x-axis.
Homework Equations
I used the disk method
The Attempt at a Solution
I drew a sketch and used disk method. For the radius I used 2-(1/2)x...
Problem
The area between y=x^{-2} and x=1 & y=e is rotating around the y-axis. What is the volume?
Attempt
\pi\left( r_{outer\mbox{}} \right)^{2}\; -\; \pi \left( r_{inner\mbox{}} \right)^{2} \; \; \; \delta y.
\frac{1}{x^{2}}=y\; gives\; \frac{1}{y}=x^{2}\; and\; r=\sqrt{y}
V=\pi...
Homework Statement
I believe this is intended to be a proof of the formula πrl, surface area of a cone.
Homework Equations
A complete volume of revolution gives you a cone - the height h is the x value on a graph, the radius r is the y value. The y intercept is zero, therefore y=r/hx ...
Homework Statement
Part c: A pendulum is attached to a 0.15m wooden bar sticked horizontally to a table by a string of 0.12m. If the system is revolved with a revolution speed of 1.5 rev per second, what is the angle θ the pendulum make with respect to the vertical axis?
Homework...