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.
Consider the solid in three dimensions that is formed when the graph of a function $f(x)$, with $f(x) \ge 0$ for all $x \in [a, b]$, is revolved around the $x$-axis on the segment $x \in [a, b]$. Derive the following formula for the volume $V$ of this solid: $V = \pi\int_a^b f^2(x)dx$. Use...
Here is my 210 word summary of the causes of the French Revolution:
The French government borrowed huge sums of money to pay for France's military support of the USA in the American Revolution. The government of France owed a huge financial debt to the French banks the French government...
So I'm getting ready for an exam on tuesday, and I'm using each method for volumes of revolutions for every problem but I'm not getting the same answers. So, let's use this as an example:
y = 5x; the shaded region is from [1,2]
Using the disk method (about the x-axis) I find:
R(x) = 5x; r(x)...
When I learned about volumes of solids of revolution, I never really memorized any formulas for specific cases per se. I used two expressions for area, either ##A = \pi (R^2 - r^2)## and ##A = 2\pi r h##.
Those expressions worked for rotations about any horizontal/vertical axis (not necessarily...
I have a few questions about finding volumes of solids of revolution (in a typical first year single variable calculus course).
1) I can rotate any region about any horizontal/vertical axis. How exactly do I rotate a region about a line that is neither horizontal nor vertical (##y = x - 1## for...
I was wondering if anyone could help me with this. I'm stuck and not sure where to start/how to go about it and finding the integral as well...
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y=5x^2,x=1,y=0, about the x-axis
Homework Statement
The area under y = (x^2/9) + 1 from x = 0 to x = 3 , and the area enclosed by the y= 0 , y=2 , x=3 , and x=4, are rotated about the y-axis , and the solid generated represents a metal ash tray , the units being cm. Calculate the volume of a metal.
Homework EquationsThe...
Homework Statement
The area enclosed by y= 4/x^2 , y =1 and y =4 is rotated about the x-axis; find the volume generated.
I am really confused I keep getting (14pi/3). But the answer in the back of the book is not that at all.
An additional question, the only method I know is drawing a really...
Homework Statement
[/B]
Find the surface area obtained by rotating the curve
y = x^2/4 - ln(x)/2
1 \leq x \leq 2
Homework Equations
2π \int f(x)\ \sqrt{1+(f'x)^2} dx
The Attempt at a Solution
I can't seem to isolate for x in terms of y. I raised both sides to e and separated the exponents...
Ok, maybe I was inspired by the commercial on the Oscars tonight with Steve Wozniak, so please forgive me. Before I wax an opinion here, I'll start by establishing my street cred. I got my first Vic20 in 1982. I wrote a video game and an article that COMPUTE! magazine paid me $175 dollars...
Homework Statement
For a 0.90km radius cylinder, find the time for one revolution if "gravity" at the surface is to be 9.8 m/s2.
Homework Equations
rω^2=a
The Attempt at a Solution
i tried solving for omega but i couldn't find a solution that i only had 1 variable in it.
Homework Statement
Find the volume of the solid generated by revolving the described region about the given axis:
The region enclosed above by the curve https://webwork.math.uga.edu/webwork2_files/tmp/equations/23/88cfb3fea3d8c8579f5a0608e8bd751.png, below by the...
There is a nice equation made by Nobuo Yamamoto which describes the curve of an egg and it is:
(x^2 + y^2)^2 = ax^3 + (3/10)xy^2, where a is the length of the major axis of the egg.
Solve this equation for y, we get:
y=+/- sqrt((3/20)ax - x^2 + xsqrt((7/10)ax + (9/400)a^2))
When I rotate the...
How do planets continuously rotate on their axis or revolve around stars ? Do the energy they consume for this continued motion gets expelled as heat ?
Homework Statement
Two men with masses 70 kg and 120 kg rotate at 1 rpm on a frictionless surface and are attached by a 15 m rope.
If they pull the rope so that only 10 m is between them when they rotate, how long does it take to make 1 revolution?
Homework Equations
Angular Momentum and...
Homework Statement
Let R be the region bounded by the curves y=0 and y=x^2+x between x=0 and x=1. Compute the volume of the solid of revolution obtained when R is rotated about the axis y=-1.
Homework Equations
Disc method: integral of pi*r^2 = volume from the bounds
The Attempt at a Solution...
Our sun rotates in counter clockwise direction and hence frame dragging will be also in that direction. Suppose if we put a satellite in sun's orbit (almost circular) to revolve in opposite direction to the sun's spin, what would happen to the orbit of the satellite? Would it fall into the sun?
Homework Statement
Compute the region R in the first quadrant between y=e^(-x), x=0, and y=0. Compute using shells, the volume V of solid around the y-axis.
Homework Equations
Volume =integral of bounds 2pi*radius*height
The Attempt at a Solution
First I drew the graph. This graph really is...
A bicyclist applies varied force and velocity on their pedals as it goes around one revolution. The power distribution over one revolution is like two waves with the higher power being made on the downstrokes. The push through the bottom/top produces the lowest power. The question is does...
Find the area of the surface of revolution $y=\frac{1}{3}x^3$ from $x=0$ to $3$, about the y-axis.
$$S=\int_{0}^{9} 2 \pi x \sqrt{1+(\d{x}{y}})^2\,dy$$
$$=2\pi\int_{0}^{9} x \sqrt{1+\frac{1}{x^4}}\,dy$$
$$=2\pi\int_{0}^{9} \frac{1}{x}\sqrt{x^4+1}\,dy$$
$$=2\pi\int_{0}^{9}...
Find the area of the surface of revolution generated by revolving about the x-axis the hypocycloid $x = a \cos^3\left({\theta}\right)$, $y= a \sin^3\left({\theta}\right)$.
I'm following the textbook example, and it says that "the required surface is generated by revolving the arc from $\theta...
I encountered a problem where the answer I got was negative.
Calculate the volume bounded by $y=x^2-5x+6$, $y=0$, about y-axis.
An easy question that is best done with the cylindrical shell method:
$$V=2\pi \int_{2}^{3} x(x^2-5x+6)\,dx$$
$$V=\frac{-5\pi}{6}$$
I think I know why it's...
my final is tomorrow and my instructor gave a list of questions that will be similar to the ones on the final exam and i want to see how they should be done properly. I've been working on other problems but i can't get past these ones. thanks
determine the volume using the shell method $y=5|x|$...
Homework Statement
The top of a rubber band bushing is designed to absorb vibrations in an automobile is the surface of a revolution generated by revolving the curve z = (0.5y^2) + 2
for (0<= y <= 3) in the yz plane about the z axis.
use the shell method to find its volume...
Hey guys,
I have a couple of questions about the problem set I'm doing at the moment. Although I was able to solve most of these, I'm doubting quite a few of my responses.
http://i.share.pho.to/f7d7efe6_o.pnghttp://i.share.pho.to/82c05629_o.png
http://i.share.pho.to/d6f76bb6_o.png...
1.find tthe volume solid generated by revolving the region bounded y=sqrt x and the ;lines y=1, x=4 about the line y=1
2. using simpson rule witj n=4 to aproximate int from 0 to 1 1 over 1-x power 2 dx
https://www.physicsforums.com/attachments/69284Homework Statement
i have done the part a, for b , i use the key in the (circled part equation ) into calculator .. my ans is also different form the ans given. is my concept correct by the way?
Homework Equations
The Attempt at a...
Homework Statement
Evaluate the definite integral for the surface area generated by revolving the curve about the y-axis:
Homework Equations
Curve: y=9-x^2 about y-axis
The Attempt at a Solution
Attached
I'm having some trouble with this problem:
Find the volume of the solid of revolution, or state that it does not exist. The region bounded by f(x)= 6(4-x)^(-1/3) and the x-axis on the interval [0,4) is revolved avout the y-axis.
How would I be able to tell whether to use the shell, disk, or...
Find the volume of the solid of revolution, or state that it does not exist. The region bounded by f(x)= the square root of ((x+3)/(x^3)) and the x-axis on the interval [1,infinity) is revolved around the x-axis.
I tried using the disk method: pi* (sqrt(((x+3)/(x^3)))^2
Then I think I have to...
Homework Statement
Consider the infinite region in the first quadrant between the curve y=e^-5x and the x-axis.
Find area= 1/5 (got this part)
Compute the volume of the solid generated by revolving the region about the x-axis:
Compute the volume of the solid generated by revolving the...
Homework Statement
Calculate the volume obtained by rotating the triangle bounded by y = 0, y = x, and y = 2 - x, about the line x = -2. You may use either horizontal or vertical rectangles.
The Attempt at a Solution
So since this is a triangle, I tried to split up the volume down to...
Homework Statement
Find the volume of the solid of revolution obtained by rotating the area bounded by the curves about the line indicated.
y=x2-2, y=0 about y=-1. Need only consider part above y=-1
Homework Equations
V=∏a∫b[f(x)]2dx
The Attempt at a Solution
I'm mainly unsure of...
Homework Statement
Find the meridians and circles of latitude of a surface of revolution ##X(t, \theta) = (r(t)cos(\theta), r(t)sin(\theta), z(t))##.
Homework Equations
The Attempt at a Solution
I honestly just need a definition of what these concepts are. My book, as an aside for...
Question
I'm really having issues grasping the Volumes of Solids of revolution. I could use some help solving this question, it isn't very hard.
1. Let R be the region bounded by y = x2 and y = x + 2. Find:
a) the area of R
b) the volume of the solid if R is rotated about the...
Homework Statement
The problem is attached in this post.
Homework Equations
The problem is attached in this post.
The Attempt at a Solution
I used washer method and set my outer radius as 2+2+√(x-1) and my inner radius as 2. I set my upper limit as 5 and my lower limit as 2...
Homework Statement
The problem is attached in this post. Homework Equations
The problem is attached in this post. The Attempt at a Solution
I used shell's method and set up my integral as 2π∫(4-x)(x^2)dx, from -2 to 2 and got an answer of 128π/3 which is incorrect. The actual answer is...
"Perpetual Motion" From Satellite Revolution
This is going to sound very far fetched, and I know very little about the laws of physics, admittedly (I don't even know if I'm posting this in the right area), but curiosity compels me.
I was wondering if it would be possible to harvest energy...
Homework Statement
See the attached problem. Homework Equations
See the attached problem. The Attempt at a Solution
I used washer method and got an inner radius of x=y^2 and an outer radius of x=y+2, I calculated my upper limit as being 4 and my lower limit as being 0. The answer is 72π/5...
Homework Statement
Find the volume obtained by rotating the region between the graph of y=0.5(sin(x^2)^2) and the x-axis (from 0 to squareroot pi) about the y-axis.
The answer pi^2/4, but I don't understand how to get the answer, I can set up the integral but can't simplify it to that...
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 y-axis.
2. The attempt at a solution
v=∏ ∫ from 0 to 1 of (y-y^3)^2 dy
and doing this, I got the answer to be 8∏/105.
Did I set up that integral...
Homework Statement
Use shell method to find volume.
y=x+2
y=x^2
rotate about the x-axis
2. The attempt at a solution
I cannot seem to solve this. I thought this was the way to solve it, but I don't understand if I am missing something crucial.
This is how I set up the...
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...