Center Definition and 1000 Threads

Ive been given this table in a lecture (attached) and I'm not sure what they're using to fill in the columns of Xi an Yi, it looks like it should just be half of each section in Yi, but that is not the case in Xi, can anyone please explain this to me. Thanks =)

Wiley Coyote and his Acme rocket, together having inertia of 1000 kg, are speeding after Roadrunner. Upon seeing a large brick wall in his path, Coyote tries to slow down. Unfortunately, he’s still going 5 m/s when he runs into the wall. The wall is not affected, but the rocket crumples (the...

Homework Statement There is a section in my book that has the same title as the title of this discussion topic. I understand the math just fine, so this is a conceptual question. In the book the cross section is shaped and oriented like a C, and it shows the shear flow flowing...

I'm just learning how to use Ansys Workbench 13 to analyze static structures. I need to analyze the deformation of a simply supported beam with a concentrated force in the center vertically downward. I have a 3D model of this beam created in Solidworks. How do I create a force in the center...

When looking at example 3 in this pdf: http://www.physics.isu.edu/~hackmart/centerofmass.pdf where it shows how to find the Center of Mass of a Nonuniform Rod. I was wondering when or what you have to know in order to integrate over dm rather than changing the variables in terms of dx.

I am using the textbook called Classical Mechanics by John R. Taylor. Z = 1/M ∫ ρ z dV = ρ/M ∫ z dx dy dz On page 89, example 3.2, it says: "For any given z, the integral over x and y runs over a circle of radius r = Rz / h, giving a factor of πr2 = πR2z2 / h2." I wish the book would...

A solid is formed by rotating the region bounded by the curve y=e^(-6x/2) and the x-axis between x=0 and x=1 , around the -axis. The volume of this solid is (pi/6)(1-e^(-6)). Assuming the solid has constant density, find the center masses of x and y. center of mass (x or y)=...

Hello PF! I've got a lab on rigid body motion tomorrow, and I need help completing one of the prep questions: A rigid body is acted on by a force F through its center of mass, and also experiences a torque caused by a similar force F at radius R. At time t, what are the linear and angular...

Homework Statement Where exactly is the center of mass of a triangle ? the file attached shows a diagram of a triangle which is equilateral, and the blue spots are the mid-points of each side. Homework Equations a distance = 2/3 from the vertex (along the median) The Attempt...

1. Find the work required to move a point charge from infinitely far away to the center of a thin ring. The point charge is q= 1nanocoulomb. The rings charge is Q= 2 nanoC. The ring has a radius r=2m.Homework Equations U= qV W= -U Thoughts I think the first thing to consider is the field E...

r=acos(wt)i+bsin(wt)j is the equation(it is an ellipse) I need to somehow show that the force will always act towards the center. Is there anyone who can possibly help?

Homework Statement Why is the angular velocity of link BD the same as the angular velocity of ICD? Shouldn't it be ωICD=vD/rD/IC?

center of mass velocity greater than 1c? Basically I have two electrons moving in opposite directions towards each other. One is moving 2.5x10^8 m/s and the other is 2.0x10^8 m/s and I'm trying to use the following equation for finding the center of mass velocity: V_cm = ((p1 +...

Homework Statement You work in a plant that manufactures heavy dumbbells. Due to a manufacturing error, one side of a 100 kg dumbbell was found to be 60 kg (M1) while the other was only 40 kg (M2). The mass of the bar itself is negligible. The factory has provided you and your colleague...

what is the difference between center of mass and center of area ?? i know that they are the same for an constant density body but why ?and why they are different for nonconst density body?? thank u ,,

Hello, I was thinking of the following question: suppose we have a body in two-dimensional space and its density is described by the function f(x,y) (Note! in Cartesian coordinates!). The x-coordinate of the center of mass is given by C_x= \frac{\int\int xf(x,y)dxdy}{\int\int f(x,y)dxdy}...

Homework Statement Consider a system comprising two extended bodies, which have masses M1 and M2 and centers of mass at R1 and R2. Prove that the CM of the whole system is at [M1R1+M2R2] / [M1+M2 ] Homework Equations Definition of CM The Attempt at a Solution First I...

Two 3.00-μC charges are at the ends of a meter stick. Find the electrical potential for the center of the meter stick. V=kq/r I just want to confirm my answer here. What I did is solve this for both charges in the equation above using r = 0.5m q= 3.00 uC. So I factored out k/r...

Homework Statement A closed cylindrical canister with central axis coincident with the Z axis has a height H and a radius R. It is suspended by a rod coincident with the Y axis that passes through the canister, transecting its central axis at a height h above the bottom surface of the canister...

Hey, I am trying to solve the following problem: va=vr+ ω × rra vb=vr+ ω ×(rra+rab) vc=vr+ ω × (rra+rac) I know the vectors va, vb, vc, rab and rac and I want to know the angular velocity vector, the radius rra and the velocity vr. Physically it means that I know 3 points on a rigid...

I've been reading that the center of mass of a right triangle - the coordinates of the COM, is (1/3b,1/3h)- I can't for the life of me figure out why this is. Is there some sort of clear proof I can take a look at? I don't really know what to integrate..

I had quite a few posts about this some weeks ago, but I am still not sure about it. My question is about why you can always view the motion of an object as a traslation of the cm and a rotation around it. It makes sense in the light of the cm being the point which moves as a point particle only...

Homework Statement Assume that the Earth is a uniform density spherical mass. (This assumption is not correct but we will use it for simplicity in working the problem.) The deepest hole drilled into the Earth's surface went to a depth of 40,230 ft (Wikipedia.org). Imagine that this hole was...

A week ago I posted a thread about my conceptual understanding of the center of mass of a body. I have however not yet gained the intuition that I want, so let me ask a question about the center of mass of a spring. Consider a spring which is elongated in outer space and left to oscillate. As...

Suppose there's a hemisphere of radius R (say) and a right cone of same radius R but ht. R/2 is scooped out of it then i have to find the center of mass of the remaining part. Here's how i approached... clearly by symmetry, Xcm = 0 Now, Let M be the mass of the hemisphere so...

On finding the center of mass of a solid hemisphere i came up with some different result. Here's what i did... consider a small ring at a distance r from the center of the hemisphere and one more ring at a distance of r+dr from center of the ring. let, mass of the small element formed...

A silly doubt regarding center of mass... As we know for bodies having continuous distribution of mass we can know their center of mass by the method of integration... like, Xcm = 1/M∫x.dm but what is x here? in many cases... like in finding the COM of a ring Xcm = 0 and Ycm = 2r/∏...

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...

I don't feel I have a good understanding of what the center of mass of an object it, and what its properties are. I know it's the position of all mass elements weighted by their mass and divided by the total mass. I have learned that the center of mass moves as if it was only subject to...

When a car turns too fast, it skids away from the center and I don't understand how that's possible in terms of forces. Background idea: The confusion came about when I was approaching a question where the net force of a car on a curve was towards the center of the curve as static friction. The...

Hey everyone, first time poster, long time reader. I have two questions about a Dynamics I course I am currently taking. Because there is so much information, I have included a zipped file that contains the questions, FBD's I used, and typed up solutions (in both .doc and .docx formats) to make...

In each situation below, electric charges are arranged at the corner of a square. Each charge Q has the same magnitude with the signs indicated in the diagrams. Rank the electric potential from most positive to most negative, and the magnitude of the electric field at the center of the square...

Homework Statement A solenoid has a radius of 2mm and a length of 1.2cm. If the # of turns per unit length is 200 and the current is 12A, calculate the magnetic flux density at a) the center and b) the ends of the solenoid Homework Equations The biot-savart law: \vec{B} = \frac{\mu_0}{4...

It has been stated time and time again that the fact that galaxies are moving away from us makes us appear to be the center of the universe. Of course, someone making this observation from a different galaxy would come to the same conclusion. The implication is that any given observer in any...

What is the equation of the circle with a center point of (10, -14) when the circle is tangent to x=13? D = √(13-10)^2 + (0-(14))^2 D = √(3)^2 + (14))^2 D = √9+196 D = √205 Radius = √205 (x-10)^2 + (y-(-14))^2 = √205^2 (x-10)^2 + (y+14)^2 = 205 But how am I suppose to graph this?

Homework Statement A wagon wheel is made entirely of wood. Its components consist of a rim, 16 spokes, and a hub. The rim has mass 5.1 kg, outer radius 0.90 m, and inner radius 0.86 m. The hub is a solid cylinder with mass 3.1 kg and radius 0.12 m. The spokes are thin rods of mass 1.1 kg...

Assumptions: 1. Gravity at the center of the Earth is zero. 2. Time is slower on the surface of the Earth with respect to time in empty space (far away) Is time still affected (slowed down) at the center of the earth?

Homework Statement The density of air at height z above the Earth’s surface is proportional to e^(−az) , where a is a constant > 0. Find the centre of mass of an infinite cylinder of air above a small flat area on the Earth’s surface. Hint : Consider line density and the identities...

Consider a free rod lying horizontically in the air. Gravity produces no torque around the center of mass. Now let the rod be attached to a hinge like of that one the picture. Now the hinge provides an upwards force on the left end of the rod, whilst there is a torque effectively acting at the...

Hello everyone, Now i am trying to model wind turbine blade using solidworks. I have the airfoil coordinates at each section of the blade, but the coordinates are distance per chord (x/c,y/c) so i have to scale it using the calculated chord. When i scale it with respect to the origin -...

1. FIgures in this link: ( a donut, and a Box with and empty box inside) http://postimage.org/image/smdut3cxb/ 2.Find the CoM of the two figures 3. as i attempted for the circle: Homework Statement Homework Equations The Attempt at a Solution

Homework Statement Find the center of mass of a solid of density \delta = 1 enclosed by the spherical coordinate surface \rho = 1-cos\phi.Homework Equations The Attempt at a Solution I'm a bit confused about how to start here, mainly because the surface is defined by spherical coordinates...

I have to deal with the problem of finding an expression for the kinetic energy of a rigid body. One of its point is pivoted to a point that moves arbitrarily. So in order to find an expression for the kinetic energy I use König's theorem, but I need the velocity of the center of mass. I use...

I've been researching about this for hours at internet reading dozens of pdfs.. but can't seem to understand the concept. What does it mean if the center of mass and center of rigidity are not coincident, torsions would be produced.. can you give an example of it in more intuitive or using...

I am taking an astronomy class because I am interested in it and wanted to know more. I love all I am learning unfortunately my math skills are holding me back from getting all that I can out of this class. I realize this might not be the toughest math problem but can someone explain help me out...

can we calculate the orgin of the big bang based on the wmap and drift of galaxies?

Homework Statement The inner radius of a spherical insulating shell is c=14.6 cm, and the outer radius is d=15.7 cm. The shell carries a charge of q=1451 E−8 C, distributed uniformly through its volume. The goal of this problem is to determine the potential at the center of the shell (r=0)...

Hi all, I know that if you drill a hole from one side of the planet to the other, through the planet's center, that a particle dropped in this tunnel will oscillate back and forth forever, like a mass on a spring, with the restoring force given by gravity. What if the tunnel forms a chord...

Hello. I'm currently coding on a physics engine. To do so, I looked up some code from open-source engines. I noted that there is a function where you can apply a force to a rigid body, outside it's center of mass. It goes something like this: ApplyForceAPosition(vector force, vector...

I'd like to make a strong (~0.5 T) solenoidal field with a permanent magnet for a Faraday rotation experiment. If I take an ordinary cylindrical permanent magnet (with an axial field) and drill a hole down the center of it. What's the field deep inside at the center of the hole? Some of the flux...