Revolution Definition and 393 Threads

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...

Here is the question: I have posted a link there to this thread so the OP can view my work.

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...

Here is the question: I have posted a link there to this thread so the OP can view my work.

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...

Here is the question: I have posted a link there to this thread so the OP can view my work.

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...

Here is the question: I have posted a link there to this thread to the OP can view my work.

"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...

Here is the question: I have posted a link there to this thread so the OP can view my work.

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...

The Online Education Revolution Drifts Off Course http://www.npr.org/2013/12/31/258420151/the-online-education-revolution-drifts-off-course

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...

Here is the question: I have posted a link there to this thread so the OP can see my work.

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...

Here is the question: I have posted a link there to this topic so the OP can see my work.

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...