Revolution Definition and 393 Threads

Homework Statement The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle (r = 12.8 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is...

The Volume of a revolved function can be given by the integral of pi*f(x)^2*dx. For the arc length of a graph, a different integral is available. I understood the proof of these two and their integration is understandable. From such, I was actually expecting that the surface area of...

Homework Statement A car engine accerlates from 1080rpm to 4800rpm in 12.5 seconds. Calculate the angular accleration, assumed constant, and the total number of revolutions the engine makes in this time The Attempt at a Solution angular acceleration (a) = (wf - wi) /(tf - ti) (a)...

Homework Statement Assume that the Earth is a sphere with circumference of 24,900 miles. a. Find the volume of the Earth north of latitude 45 degrees. (hint: integrate with respect to y) b. Find the volume of the Earth between the equator and latitude 45Homework Equations circle: x^2 + y^2...

f(x) is a continuous function of x, whose domain is [a, b]. Revolve the graph around the x axis. In doing so you will create a solid. Apparently, to find the volume of this solid, partition the solid into n cylinders along the x-axis from a to b, each partition of the x-axis containing some...

[SOLVED] Area of a Surface of Revolution--Help Please 1. Problem: The curve y=e^(-x), x>0 is revolvd about the xaxis. Does the resultin surface have finite or infinite area? [Remember tht you can sometimes decide whether improper integral converges w/out calculating it exactly] 2...

Homework Statement Find the surface area obtained when the upper half of the ellipse: \frac{x^{2}}{4}+ y^{2}=1 is rotated about the x-axis Homework Equations \int2piyds The Attempt at a Solution

Mean Value Theorem to calculate solids of revolution? Ive been studying calculus on my own because my school doesn't offer it and i came across solids of revolution tonight. In one of the problems it says "What is the volume of the solid formed by rotating y=e^x across the x-axis between...

This may be a weird question, but oh well. Way back during the Scientific Revolution it would have been possible to define mass as acceleration divided by force right? Then you'd have F = a/m, and the units for force would be different than they are now.

[SOLVED] Dynamics of Circular Revolution Homework Statement In another version of the "Giant Swing", the seat is connected to two cables as shown in the figure View Figure , one of which is horizontal. The seat swings in a horizontal circle at a rate of 33.1 rev/min If the seat weighs 252 N...

the question is.. Find the areas of the surfaces generated by revolvin the curves about the indicated axes. x = (1/3)y^(3/2) - y^(1/2), 1≦y≦3; revolved about y-axis so i use the general formula "S = Integral 2π (radius)(dS)" and the radiu in this case is x which is (1/3)y^(3/2) -...

[SOLVED] Volumes of Revolution Homework Statement find the volume of region A in the first quadrant that is inclosed in the parabola 2x(2-x) and the x-axis, of which is rotated around the axis y = -2. Homework Equations y=(4+2x^2) y= -2 piS(from 0 to 2) (R^2 - r^2) The Attempt at...

Hi! More than a decade ago, I used to listen to a so-called walking encyclopedia over the radio. One of the radio listeners verified the information that he had read somewhere: That if the Earth revolved on its axis at a much faster rate, then time would become faster. However, this radio...

[SOLVED] Washing Machine revolution Homework Statement A tub of a washing machine goes into it's spin cycle , starting from rest and gaining angular speed steadily for 8.00s, at which time it is turning at 5.00rev/s. At this point the person doing the laundry opens the lid and a safety...

The problem below is actually in reference to determining the location of a unknown gamma radiation source. However, I believe the solution lies with relatively simple calculus. First, the equation that defines the relationship between the radiation exposure rate and the distance from the...

Homework Statement I need to know how to convert angular speed into revolutions Homework Equations W=2*pi/60 sec, but that's for rad over second The Attempt at a Solution w=2*pif

Homework Statement The problem is that an ellipse (centered at origin) is revolved about y-axis. Now I have to find the volume of this swept region. But how do I go about using calculus? I have to derive it. Homework Equations Volume of ellipsoid = 4/3*pi*abc (source wikipedia) Equation...

Homework Statement Compute the volume of the solid formed in the first quadrant by y=x^4 and y=125x when rotated around the x axis. Homework Equations the integral for a disk is solved by taking the integral from a to b of pi R^2 The Attempt at a Solution I found the...

all says electrons rounds the nucleus and revolves in its own axis if so in which direction electrons rounds the nucleus?

1. find the area common to r=1+cos@ and r=3^(1/2) sin@ 2. find the volume generated by rotating the region bounded by (x-1)^2 + (y-2)^2 = 4 around a. x axis b. y -axis c. x = 3 d. y = 4

Rate of revolution for a dryer?!? Homework Statement In a home laundry dryer, a cylindrical tub containing wet clothes is rotated steadily about a horizontal axis as shown in the figure below. So that the clothes will dry uniformly, they are made to tumble. The rate of rotation of the...

Consider the ellipse: (\frac{x}{2})^2 + y^2 = 1 We rotate this ellipse about the x-axis to form a surface known as ellipsoid. Determine the area of this surface. Start off by solving for y. y = \sqrt{1-\frac{x^2}{4}} Then find the derivative. y' =...

I have tried this question (http://img524.imageshack.us/img524/9539/scan0001pa1.png) a number of times and always use the formula S = 2*pi*int( y*sqrt( (dx/dt)^2+(dy/dt)^2 ) dt i always get S=6*pi*a^2[1/5*(sin t)^5] 0<t<pi, and because sin 0 = 0 and sin pi = 0 the answer i get is 0. If you...

Period of rotation and revolution of moon is same (w.r.t. distant star), that's why we can only view only one face of the moon. Cosmological fact or reasonable science?

Find the volume of the solid of revolution obtained when the region under the graph of f(x) = \left( \frac{1}{x} \right) e^\frac{1}{x} from x = 1 to x = 6 Homework Equations \pi \int (f(x))^2 dx The Attempt at a Solution Ok, the equation I gave above should be that...

In the past we had single man revolutions in theoretical physics like Galileo, Newton, Einstein. Will there likely be another figure as big as them today? Or will today be more groups of people building up their ideas rather than a single person producing all the big ideas?

If f(x) = x to a power between -0.5 and -1, the area between the f(x) graph and the x-axis from, say x=1 to infinity is infinite, but the volume of revolution of f(x) around the x-axis is finite. This seems counter-intuitive. Can anyone give a satisfying explanation of this - preferably a...

Homework Statement Find the volume of y = 2x^2 y = 0, x = 2 when it is revolved around the line y = 8.Homework Equations Integral formulas for volumes by discs, washers and cylinders.The Attempt at a Solution Translate the curve so that axis of revolution is along the X axis. Is this the...

Suppose that you have a parametric curve given by x = f(t), y = g(t), a ≤ t ≤ b What will the Surface of revolution and Volume of revolution around the x-axis be? I have two candidates: Surface: S = 2*pi*int( |g(t)|*sqrt( (df(t)/dt)^2+(dg(t)/dt)^2 ) , t=a..b) Volume: V = pi*int(...

here is the question: The finite plane region bounded by the curve x*y=1 and the straight line 2x+2y=5 is rotated about that line to generate a solid of revolation. Find the volume of solid. İ have to do this on mapple can someone help me how can i do this.

Homework Statement Find the volume generated by rotating the area bounded by y=2+x and y=x^2 about the y-axis. Homework Equations Volume of revolution. The Attempt at a Solution shell method integral (0 to 2) of x(2+x-x^2) dx I think this can be solved by eliminating the left...

Homework Statement Find the volume generated by rotating the area bounded by y^2 = 8x, x = 2 and the x-axis about the y-axis. Homework Equations Volume of cylinder, volume of disk. The Attempt at a Solution I think this can be solved by subtracting the 'empty' volume from the...

What'll become of Earth if it stops revolving around: 1)Sun in its orbit. 2)Its own axis. Also if gravitation of both Earth & sun is zero what impact'll be upon their condition? N.A No

(my first dealings with latex.. so bare with me if this looks a little messed up at first :rolleyes: ) Homework Statement Find the surface area for the equation: x = 3y^{4/3} - \frac{3}{32}y^{2/3} with bounds -216 \leq y \leq 216 rotated about the Y-axis. Homework Equations \int^a_b 2\pi...

Homework Statement A wheel accelerates from rest to 59 rad/s at a rate of 29 rad/s². How many revolutions the wheel turned while accelerating?Homework EquationsThe Attempt at a Solution I'm confused, I suck at this kind of problem. I got change in angular velocity which would be 59rad/s, and...

Homework Statement Write the equations of a surface of revolution with axis OZ: A) the Torus obtained by a rotation of a circle x= a + b*sin(u), y= 0, z = b*sin(u) 0 < b < a B) the pseduosphere obtained by the rotation of a tractrix x= a*sin(u), y=0, z= a*(log(tan(u/2) + cos(u))...

hey since the Earth turns around itself , turns around sun, sun turns around galaxy, galaxy is in movement (or maybe orbiting something bigger, who really knows ?) Well with all these movements, our velocity must be close to c ? thus , what is galaxy turns around ..., which turns around...

Homework Statement Hi, the next problem I thought it was easy...and I really think it is, but I haven't come with the right answer :S. I compare the answer in an internet page of problems and all it says is "wrong"... The problem is the following: Find the volume of the solid obtained by...

A minor Immirzi scuffle (Corichi, Ghosh, DeBenedictis) Andrew DeBenedictis and two friends just came out with a paper that will stir up Immirzi controversy. http://arxiv.org/abs/gr-qc/0702036 Already there have been series of papers on the one hand by Corichi et al and on the other by Ghosh...

Homework Statement "The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method." y=5, y=x+4/x; about x=-1 Homework Equations Upon plotting it I decided it would be best to use the shell method. I'm not sure how to...

Homework Statement Find the area of the surface obtained by rotating the curve about the x-axis: y=cos 2x, 0<=x<=pi/6 Homework Equations Surface area about the x-axis = Integral of 2pi * f(x) * sqrt(1+[f'(x)]^2) dx The Attempt at a Solution I think I set up my integral correctly, so...

The question I need to solve for an assignment is as follows: Find the volume of the solid that is obtained by revolving the region R around the x-axis. I figured that the volume would just be the integral of pi R^2 dx, so that would just be pi R^2 x, but that is not the answer. I suspect I...

Anyone have any advice for finding volumes of solids that are not solids of revolution? I have a much more difficult time starting these kinds of problems compared to revolving ones.

What is the volume of the figure bounded by y = 2x - x^2, y = 2x, x = 2, and rotated about the line y = -1. Is this the correct integral? \[ V = \pi \int_0^2 {((2x + 1)^2 - (2x - x^2 + 1)^2 } )dx \] Thank you for your time.

Why doesn't a satellite's radial velocity (falling toward the Earth's center of gravity) increase as it it revolving --- I understand why its tangential speed stays the same but what is stopping the satellite from accelerating in its fall -- there is no air resistance up there. In other words...

Hello, I have a few questions concerning what the atomic model currently "looks like" since the quantum revolution. I know that, since the wavefunction, electrons are in probability "clouds" and I know they are standing waves. So this would mean, technically speaking, that the electron...

Rotate about x-axis the region enclosed by y=e^x, y=1/x, x=1 and x=2. I can do the problem with the rings method but I don't how to even set up the integral to solve by the shells method. Help? Thanks

Hey, I ran into a few things about angular quantites and am a little confused on finding the number of revolutions something such as a tire would make. Would the distance traveled divided by a circumference of a circle equal the number of revolutions? I was finding that there are equations that...

to any and all the player

If U [i.e., set theory] were to be equippable with a vector space type morphology...Prolly more of a module than a v.s.. Yes, a field over a ring, perhaps, if that's possible... dim(U)...: 0. emptiness 1. isolation 2. expansion 3. containment 4. transition 5. hyperspace 6...