Homework Statement
if a disc of mas m is pure rolling , with velocity v .
the instantaneous axis of rotation would be the point of contact with the ground .
As shown in the diagram this could be considered as a disc rotating about one of the point on circumference for an instant of time ...
Homework Statement
y = {\frac{1}{4+x^2}} on the interval [0,2], revolving about y = -1
Use either the disk/washer or shell method to find the volume.
Homework Equations
v = pi\int (outer radius)^2-(inner radius)^2\,dx
v = 2pi\int (radius)(height)\,dy
x = \sqrt{\frac{1}{y}-4}...
Hi, this isn't really a homework problem... but I'm just wondering
I see the time axis as c*t, now people say that its to scale the time axis so that the world line of light is 45 degrees. But if you were to multiply time by the speed of light, wouldn't you just get the units metres or...
Hello,
Can some explain to me how to calculate the power coefficient of a vertical axis wind turbine.
If you explain the steps invloved would be great or any external file location where I could refer.
I have below information
1) Lift Coefficient.
2) Drag Coefficient.
3) Angle of...
I can easily visualize the 3 dimensional way to do so, and already have.
I'd like to rotate from the (-1,-1,-1,-1) -- (1,1,1,1) line to the x-axis (-1,0,0,0) -- (1,0,0,0).
To do so in 3 dimensions (-1,-1,-1) -- (1,1,1) line to the x-axis (-1,0,0) -- (1,0,0)
I rotated around the z...
1. Homework Statement
http://session.masteringengineering...bs._454_55.jpg
Find the moment about the axis AC. F=<7,12,-6>
2. Homework Equations
MomentAC = Uac dotted with (Rab X F)
Uac is the unit vector from a to c
3. The Attempt at a Solution
Uac=<.8,.6,0>
Rab=<4,3,-2>...
Homework Statement
http://session.masteringengineering.com/problemAsset/1127287/7/Probs._454_55.jpg
Find the moment about the axis AC. F=<7,12,-6>
Homework Equations
MomentAC = Uac dotted with (Rab X F)
Uac is the unit vector from a to c
The Attempt at a Solution
Uac=<.8,.6,0>...
Consider a freely rotating body. Let the axis of rotation be the z-axis. For simplicity assume all the mass of the body is concentrated in the x-y-plane, i.e. the plane in which the body rotates.
I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine...
Says Wikipedia: "The moment of inertia is a measure of an object's resistance to any change in its state of rotation".
Now consider a rotating mass m that I would like to accelerate along its axis of rotation by a. Does this count as a "change in its state of motion"? Will it resist the...
Hi i have cylinder geometry . bottom (cross section)circle centre point is x1, y1, z1 and top is x2, yz, z2. cylinder centre axis is not allign with any (Global x,y,z) axis. if i want to align a cylinder with Global axis(x,y,z), what is angle need to rotated with respect to x ,y ,z (Global )axis.
Homework Statement
Determine the magnitude of the moment of the force F about the axis CA of the tripod
ABCD, if F = {40i -30j -100k}N.
Image attached.
2. The attempt at a solution
Based on a similar question I found in the textbook my method to solve this question:
Find UCA =...
A 180 degree circular arc (i.e. a half sphere) is obvious:
When you rotate this about its two end points, you get a sphere.
What about for something less than 180 degrees (e.g. 90)?:
I believe this forms an ellipsoid, with coefficients a and b being equal, with respect to...
Torque is defined as:
τ = rxF
this means that the farther from the rotation axis of a body a force is applied, the more it will tend to rotate the body.
My question is:
Can anybody give me a simple argument that a force applied farther from the rotation axis should be better at...
Homework Statement
A uniform sign is nailed into a wall at its top two corners. The nail on the upper-right corner breaks, and the sign begins to rotate about the remaining nail in the upper-left corner. The mass of the sign is 69 kg, L (length) = 1.6 m, H (height) = 2.2 m, and the moment of...
A 3-dimensional graph has infinite number of derivatives (in different directions) at a single point. I've learned how to find the partial derivative with respect to x and y, simply taking y and x to be constant respectively. But what do I do if I want to take the partial derivative with respect...
Homework Statement
A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center?
Homework Equations
Ip = Icm + Md2
Isolid sphere = 2/5MR^2
The Attempt at a Solution
This is...
I can work out the acceleration of a block that will take along the plane when the axes are the ones along and perpendicular to the inclined plane. But, when I choose a horizontal and vertical axis I end up with the same mistake as this guy in this thread did...
Homework Statement
Homework Equations
The Attempt at a Solution
So this isn't a specific question, I'm just having trouble with my definitions.
In my book for f(x) = (x - 2) ((x + 1)^2) (x-4) it says that the zeros are at x = 2, -1, 4.
On the page it shows that the graph doesn't cross the...
Homework Statement
Hi
I have a question - it is not homework, but something I have thought about for a long time. I really can't come up with a solution to the problem, and it is driving me crazy. Here is the problem:
Say I have a linearly polarized monochromatic wave incident on an...
A vertically moving object projectile reaches a maximum height of 50 meters above its starting position
What is the projectiles initial speed?
What is the height above the starting point at 3.3 seconds?
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
Note: The following are taken from Physics for Scientists and Engineers 6E
http://img542.imageshack.us/img542/821/75796098.png
http://img152.imageshack.us/img152/5615/70724407.png
http://img804.imageshack.us/img804/6813/65815357.png
I don't really understand why is that integral...
Homework Statement
The area bounded by the x-axis and curve
y = 4-x^2
is rotated about x-axis, find the volume.Homework Equations
[integral] pi y^2 dxThe Attempt at a Solution
the answer is supposed to be 512/15 pi
Homework Statement
A uniform rod of length l is given an impulse at right angles to its length as shown. Find the distance of instantaneous centre of rotation from the centre of rod.
Homework Equations
The Attempt at a Solution
Impulse=change in momentum
or Impulse=mvCM (Am i...
Its stated that total energy of an isolated system is given by
E = \frac{1}{2}mv^{2} + \frac{1}{2}Iω^{2} + mgh.
Whats the correct form when the velocity is along 2 axis, that is, along x and y-axis like v = (2, 1)?
Should the resultant be taken or just add the kinetic energies along each axis...
Hello! I'm not sure this is the right place to ask, but i have a huge problem. I have an axis and it's origin, and also a point. I suposed that is enought to describe an ellipse, but how to do so? I want to describe it by having it's center and both it's radius. Some images to ilustrate what I...
I need to track Distance on one Axis with an Accelerometer for a rocket project (i know there are bettor ways t do this but i am dead set on this one) I was thinking as follows,
Read Accelerometer
Accelerometer*Δt=Δv
Current speed+Δv=New speed
distance+New speed*Δt=New distance
Hello,
I'm trying to define an axis as a set of 3 unit vectors--u, v, and w. at a given point P
Suppose we are given the following vector u. From this vector u, we must define a plane such that u is normal to the plane. This plane will be represented by two perpendicular vectors v and w...
Hi
Please see the attached picture. It shows an atom, the filled black circle, which consists of a J=0 level (with m=0 sublevel) and J'=1 (with m' = +/- 1 sublevels). From the left is a nearly monochromatic laser impinging on the atom, which is linearly polarized along the same direction of...
Homework Statement
Answers in the back of the book
about x-axis= 190
about y-axis= 828Homework Equations
Simpson's Rule: (dx/3)* sum of(sequence of coefficients {1,4,2...2,4,1}*sequence of function values{f(0), f(1), f(2)...f(n-2),f(n-1), f(n)})
Volume using Shells: 2π ∫ (radius)(height) dx...
All of you may have heard this. Without the Moon, Earth's axis would fly wildly out of control due to the other planets' gravity. Now, that makes sense, the Moon giving a stabilizing effect. But what confuses me is why Venus and Mercury both have near 0 degrees of tilt. They don't have a moon to...
Homework Statement
A meter stick is held to a wall by a nail passing through the 60-cm mark. The meter stick is free to swing about this nail, without friction. If the meter stick is released from an initial horizontal position, what angular velocity will it attain when it swings through the...
I've been reading a few books on scattering of light from particles, in particular mie scattering of cylinders. At first I want to look at infinite cylinders, then finite cylinders once I understand a bit better.
The problem is that all of the books I've looked at treat the problem where...
Hi there, first post on these forums. I have a seemingly simply question about beam bending.
We (mechanical engineers) are all very familiar with the standard beam bending scenario. The beams are always shown being loaded perpendicular to the neutral axis, regardless of the type of support...
hey guys,
I have a problem I need to solve for my masters thesis. I have an object that rotates in 3D space. There is no translation. Given that I have coordinates of one landmark at 2 instances of time I need to calculate axis of rotation and angle of rotation.
is this sufficient...
Hi,
how can i change x and y-axis scale to make sure that x and y-axis are on the same scale in matlab?
my x-axis is from 0 80 but the y-axis is from -3 to 5, so in plot the axis are not the same but i want to have same scale on both axis.
Thank you.
Hello,
From what I've read, I understand that a spinning disc has a torque which resists the tilting of the disc's axis. From what I understand, the higher the angular velocity of the disc is, the more the disc will resist tilting. Can anyone tell me how to calculate this torque? If there is...
Hi,
I would be happy if you could solve and explain following problem:
Imagine some solid long object (wooden plank for example) being just like that in vacuum, free, without being fixed to any point of space.
Then, imagine only one forse pushing this object in a certain point of object...
Homework Statement
evaluate the integral:
I_1 =\int_0^\infty \frac{dx}{x^2 + 1}
by integrating around a semicircle in the upper half of the complex plane.
Homework Equations
The Attempt at a Solution
first i exchange the real vaiable x with a complex variable z & factorize...
When i apply torque on a body, it will rotate around whcih axis? I guess its the axis along centre of mass but i don't know why?
Also if the answer is centre of mass what will be the orientation of the axis- I mean there are infinite lines passing through a single point so which of those...
Homework Statement
Find the moment of inertia of a uniform disk of mass m and radius r about an axis normal to the disk, through a point x from the centre.
Homework Equations
The Attempt at a Solution
Let ρ be the density. I=ρ∫r^2 dA=ρ∫∫r^3 dr dθ in polar coordinates.
However I...
Please consider
http://gyazo.com/e5c5b4f7808a63e7e664440259ac3058
I agree with all notes made on that slide, but I don't actually get how they constructed the diagram from that? I understand that they line represents frequency so going to 0 to infinity means the line would travel from -0.5 to...
1. Problem I am attempting to model the dynamics of the system shown in the attached image. I have a DC Motor with two disks attached to it via springs and something similar to a servo horn. I have two questions. The first is how to determine the inertia of the disk and the spring about the...
Homework Statement
y=x^2+1
X in (0,1)
Homework Equations
formula needed
integral (PI [f(x)]^2 DX
in the F(x) just plug in the equation right?
The Attempt at a Solution
took anti deritive of the original problem and came out with
PI[1/3x^3+X]^2
my answer is 5.58
am i on...
Hi,
I need some help, I have a system with 3 cylinders (I got the center of mass for the system). Now I need to calculate the moment of inertia for the system.
I have tried to find some examples or general information, but they all show when the axis either is centered within the object or...