Revolution Definition and 393 Threads

In today's Physics ArXiv: FROM TIME TO TIMESCAPE – EINSTEIN’S UNFINISHED REVOLUTION Dark Energy as simply a mis-identification of gravitational energy gradients and the resulting variance in clock rates? David Wiltshire's Abstract: Garth

I know that the surface area of a revolution is equal to the integral from a to b of 2pi times the radius time the arc length. But, why isn't it just the integral from a to b of the circumference?

i need someone to explain to me where i am making a mistake because i am getting an answer that differs from that of the book. the solid lies between planes perpendicular to the x-axis at x = 0 and x = 4. the cross-sections perpendicular to the axis on the interval 0 ≤ x ≤ 4 are squares...

Find the volume of the solid y = sinx, y=cosx, and x= pi/4, revolving around x-axis I didn't really get this at all... do I plug pi/4 for x in y=sinx, y=cosx to get the integra boundaries?

A log having the shape of a right circular cylinder of radius a is lying on its side. A wedge is removed from the log by making a vertical cut and another cut at an angle of 45 degrees, both cuts intersecting at the center of the log. Find the volume of the wedge. And as soon as I finish...

How can i get the volume of this problem Homework Statement y = cosx, y = sinx , x = pie/2 , and the y-axis finding the volume about x & y axis

Homework Statement I am writing a paper on volumes of revolution. Unfortunately I haven't been able to find any suitable programs to represent them graphically. (I apologize if I am posting in the wrong forum.) Homework Equations Graphing the volume of revolution of, say...

Let us consider the revolution of the moon around the Earth. If the moon was expanded like a balloon so that it had the same mass but different volume (and therefore lower density), would it effect the moon's revolution in any way? I probably sound like a retard right now...:confused:

My textbook notes that if: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}}=1 and a \neq b \neq c Then the ellipsoid is not a surface of revolution. It seems to me though that one can always find a curve in the plane, which when rotated around a line will produce the...

(EDITED) 1. Use the shell method to find the volume of the solid generated by revolving about the y-axis. x=y^2, x=y+2 2. same as #1, except change y and x for the two equations and revolve about x-axis. I tried doing 2pi\int_{x=0}^4(x)(\sqrt{x}-x+2)dx but the answer is off for #1. I...

(EDITED) 1. Use the shell method to find the volume of the solid generated by revolving about the y-axis. x=y^2, x=y+2 2. same as #1, except change y and x for the two equations and revolve about x-axis. I tried doing 2pi\int_{x=0}^4(x)(\sqrt{x}-x+2dx but the answer is off for #1. I tried...

Homework Statement given z =y3 revolved around the y-axis what is the equation of the surface and then graph. Homework Equations The Attempt at a Solution I have no idea how to approach this, i tried searching around the net but nothing came out. pls help.

To what extent was the French Revolution preventable ?

Please Help! - Integration, Rate of Change, and Volume of Revolution Questions Hi I have completes these following questions but am not sure if I have done them correctly as it is a long time since i studied these topics. I would really appreciate any help. :-) 1 Simplify the following as...

How will future biographies differ from those past, given the proliferation of electronic data?

Can the Surface area of a revolution be NEGATIVE? I am calculating this in parametric equations? finally I hope this is the right forum to ask this question.

Can the Surface area of a revolution be NEGATIVE? I am calculating this in parametric equations? finally I hope this is the right forum to ask this question.

does the Earth rotate and undergo revolution with the same speed?is the rotation and revolution in same direction

Homework Statement An ellipse is rotated around the y-axis, find the volume of this solid. Homework Equations x^2 / a^2 + y^2 / b^2 = 1 \pi\int_{a}^-a x^2 dy The Attempt at a Solution I'm having trouble solving this; I know that the upper and lower bounds of the curve occur on...

Homework Statement 1. Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y= \frac{1}{x}, x = 1, x = 2, y = 0 2. A solid is generated by revolving the region bounded by y =...

Homework Statement Find area of surface generated by revolving about x-axis. y=x^3/3 1<=x<=sqrt(7) Homework Equations find f'(x) = x^2 The Attempt at a Solution A = integral[ (x^3/3) * [(1+(x^2)^2] ^(1/2) ] ]dx = integral[ (x^3/3) * [(1+x^4) ^(1/2) ]dx I just don't know...

The volume of a cone = 1 - B H where B is the base of the cone and H is its height. 3 We can think about a cone as the line y = x rotated with respect to the y axis. The...

so i have y = 1/sqroot(3x+2) find volume when rotated around x, regions are x=2 and x=0 equation needed: V= integral Pi*y^2*dx so. i do intergral pi* (1/sqroot(3x+2))^2 * dx so i get pi integral 1/(3x+2) dx so how do i integrate 1/sqroot(3x+2) ? can someone take me...

Is there a simple or generalized way (formula) to generate the radius of a solid of revolution? How does the orientation of the function relative to the axis of revolution affect the radius (radius= 4-f(x) or 4+f(x))? Why is the radius sometimes only x or y , and other times some other function...

Write a definite integral that gives the volume of the solid of revolution formed by revolving the region bounded by the graph of x = e^(−y^2) and the y-axis between y=0 and y=1, about the x-axis. Not sure how to set up the problem

Hi, I've been plotting potentials and electric fields inside and outside shells; when I create 2 separate RevolutionPlot3D plots for the potentials (1) inside the shell and (2) outside the shell, I'd like to combine them into one plot. I tried using the Show function, but Mathematica doesn't...

http://img15.imageshack.us/img15/858/masteringf.jpg a: 550-150 = 400rev change 400/60 = 6&2/3 rev/s (converted to revs) 6.66666 / 3.5 seconds = 1.9 rads^-2 since it's decelerating i put -1.9 rads^-2 now part two i got wrong, b: \thetaf=\thetai + \omegai * t +...

Homework Statement A doubly charged helium atom whose mass is 6.6 \times 10^{ - 27} {\rm{kg}} is accelerated by a voltage of 2800 V. What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.370 -T field? What is its period of revolution?Homework Equations F=qvB...

In my Cal II, we're discussing finding volumes of revolution using centroids, which we find using moments of x or y. Can someone explain to me what a moment is?

Homework Statement Earths´ satellite orbits 4200km above Earths surface. Count satellites´ trajectory circle-shaped and calculate satellites´period of revolution. The Attempt at a Solution I added the Earths´ radius to the 4200 km, which represents the orbiting attitude and then my mind...

Homework Statement Consider now a shape that is obtained by revolving the “infinitely long” function f (x) = 1/x , 1 ≤ x < ∞ around the x-axis. Find both the surface area of the resulting object, and the enclosed volume of it, i.e. the volume of the solid obtained from revolving the...

Homework Statement I have to go around and find the volume of a silo-shaped trash can using solid of revolution height 91cm Circumference 119.3cm Diameter 15cm http://common.csnstores.com/United-Receptacle-European-Designer-15-Gal.-Round-Top-Receptacle~img~UR~UR1180_l.jpg is what the...

y=x^2 ; y=4; rotated around x=2 im seeing a washer cross section with r=2-y^(1/2); im unclear on how to get R to calculate the area it seems to be 2r but this produces incorrect results.

I just finished reading Niels Bohr's times: In Physics, Philosophy and Polity by Abraham Pais. It is an amazing book on the life of an extraordinary genius. This book really got me thinking into the state of physics in the 21st century. The last great discovery, unless I am mistaken, was the...

Hi guys, I did post this over on the h/w c/w forum last week, but I think actually it is out of the scope of that, plus its not actually h/w c/w, its my general wondering :D So I am having an issue with the volume of a sphere and calculating it. I am using the method where the solid, sphere...

Homework Statement Let R be the region bounded by the graph y=(1/x)ln(x), the x-axis, and the line x=e. Find the volume of the solid formed by revolving the region R about the y-axis. The interval should be (on the x-axis) from 1 to e and from the y-axis, it should be from 1 to (1/e)...

Hello folks, I was wondering how to set up a volume of the solid of revolution about a line in the form of a line equation. if i wanted to find the volume about a line of x/4 would I simply find it as v=pi*integral (f(x/4)^2)dx or is there a method I'm missing all togeather?

Homework Statement y = sin \pix Using arc length and surface revoultion on x-axis 0 <= x <= 1 The Attempt at a Solution d/dx sin \pix = \pi cos \pix (\pi cos\pix)^2 = \pi^2 cos^2\pix \int sin pi * x * 2 * pi * \sqrt{1 + pi^2 * cos^2 (pi*x)} u = pi cos (pi * x) du = -pi^2 * sin...

Homework Statement The curve 3x2+2y2-12y=32 is rotated about the x-axis and forms a solid hemisphere. Verify that the weight is 8cm from the bottom of the hemisphere. Homework Equations The Attempt at a Solution Now, I can only do a little bit in centroids but that is for...

Homework Statement Im doing a philosophy, history and politics of science subject and the question is whether gravity was waiting to be discovered or was it an intellectual construct particular to the 17th century and Newton. Homework Equations The Attempt at a Solution I'm...

Hello ppl. I have a problem in finding out the volume of solid formed by the revolution of one loop of lemniscate of bernoulli ( r²=a²cos2θ) about the initial line θ =0 Using the relevant forumula for the volume of the solid generated by the revolution of one loop of the polar curve about the...

[b]1. Find the volume of the solid generated by revolving the region bounded by the x-axis and one arch of the cycloid x=theta-sin(theta), y=1-cos(theta) around the x-axis. [b]2. hint:dV=(pi)y^2 dx [b]3. So far I have been unable to solve for theta so that I can form a relationship...

Homework Statement http://65.98.41.146/~grindc/SCREEN01.JPG Find the volume of the solid generated by evolving the region bounded by y = sqrt(x), y = 0, x = 4, when revolved around the line x = 6 Homework Equations The Disk/Washer Method - The Attempt at a Solution let R(y) =...

I've encountered a weird problem in my text...somewhat by accident =P My text only covers volumes of revolution through the disk method, and one of the questions was: Find the volume of the solid obtained when the given region is rotated about the x-axis. c) Under y = 1/x from 1 to 4 Using...

Homework Statement Find the volume of the solid obtained by rotating the region under the graph of y=1/x and y=1/x^2 about the vertical axis x=-1 Also given are points on the y-axis (0,2) and (0,5). I guessing these points are specific sections of the graphs where we find the volume...

Homework Statement This project deals with custom made gold wedding bands. Its shape is obtained by revolving the region shown about a horizontal axis. The resulting band has Inner radius R, Minimum Thickness T, Width W. The curved boundary of the region is an arc of a circle whose center...

Homework Statement The area enclosed between the ellipse 4x^2 + 9y^2 = 36 and its auxiliary circle x^2 + y^2 = 9 is rotated about the y-axis through \pi radians. Find, by integration, the volume generated. This is the whole question. I assume it means bounded by the x-axis, but even if...

Hi there, I have no idea about this question can anyone help? S is a solid of revolution in 3-dimensions, formed by rotating a full turn about the y-axis, the region in the first quadrant of the (x, y)-plane bounded by the interval [1, 2] on the y-axis, and the curve x = (2 − y)(y − 1)^2...

hi I'm super stuck with this question: I'm super stuck with these two problems on one of my practice exams, can anyone help me out? Find the integral between 4 and 3 of (u^2 + 1) / (u - 2)^2 and Find the volume of the solid of revolution obtained by rotating, a full turn about the...

help my final is friday and law school depends upon it.volume of revolution (VOR) for base of x^2 + y^2=25. Assume the square slcies are Peripindxular to the x axis. voR for area between y=2x and y=2cos x revlved aroung the line y=-50 write definite integrals and evaluate thanks in advance