Revolution Definition and 393 Threads

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)...

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...

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...

Ok the answer in the back of my book says 974 revolutions and a very short hand way to get that is divide the big wheel radius by the small wheel radius to get 3.53 so i can just multiply 3.53 times the 276 rev to get 974 rev. But I tried a long way using the s=rtheta formula b/c on a test I...

1. Consider the function f(x) = arcsin(2x^2 - 1). Write down, but do not attempt to solve, a definite integral in terms of y, which when evaluated will give the volume of the solid of revolution formed by rotating the graph about the y-axis. 2. Endpoints are at (-1, pi/2) and (1, pi/2)...

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...

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...

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

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*...

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...

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...

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...