Center Definition and 1000 Threads

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...

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...

Homework Statement Find the position of the center of mass for a thin sheet and homogeneous, with sides R and 2R ,from which has been subtracted a half circle of radius R. [Xcm=(2/3)*R*(4-pi)]Homework Equations Rcm=(1/M)*∫rdm The Attempt at a Solution By symmetry we know Ycm=0. For de...

I have a question about a spinning spool, there is a spool spinning and is the sistance traveled by the circumference the same as the center of the circle? You can refer to the diagram attached for a question I had trouble with from a physics olympiad. The answer was (B). Thanks in advance!

Homework Statement Given a homogenous rectangular surface, sides of length a and b=4*a, with a circular hole in x=a and y=a/2, find the center of mass. Homework Equations R=1/M*Ʃmi*ri , M= total mass, r= position vector area of a circle = pi*r2 , r being the radius The...

Homework Statement A mass of 200 kg is hanging directly in the center of a chain; the chain makes a 20o angle from its horizontal. The chain will break if more than 2000 N of force are applied at any point on the chain. Will the chain break?Homework Equations F=ma Tfy=mg(sin\Theta) g=10m/s The...

We all know the proof, from Newtonian mechanics, that the motion of the center of mass of a system of particles can be found by treating the center of mass as a particle with all the external forces acting on it. I want to prove the same think, but within the framework of Lagrangian mechanics...

Hello! I'm here again, now with a new exercise! :biggrin: Homework Statement A block of mass m is at rest over this wedge (it's a triangle) of mass M that is at rest over a table. There is no friction. The point P of the block has a height h from the table. Then the block starts to move. What's...

Homework Statement a toy which have a shape of tank (military vehicle) has a platform of 192mm long, 140mm wide, weight of 2075grams. The canon is 239mm long, 50mm wide, and weight of 400grams. the canon is on top of the platform and being assembled 58mm from the front side of platform. where...

Probably a stupid question as I'm sure we don't but stargazing gets me thinking. The last prevailing theory that I heard of was a massive black hole at the center of the milky way (and all other galaxies). However, the core of the galaxy is the brightest part by far and other than extremely...

Homework Statement I'm trying to understand the equations given in my textbook (Principles of Physics, Ninth International Edition) for finding the center of mass. The equations are given below. They're used to find the x, y, and z components of the center of mass for objects. I'm trying to...

Hi. Just like in classical mechanics, I've read that in relativity, the velocity v of a particle just reverses after an elastic collision in the center of mass. I.e, if v is the velocity before the collison and v' is the velocity after, then v = -v'. I wondered how one goes about showing this...