Center Definition and 1000 Threads

In absence of any other forces, if you push a free object not on the center of mass, during the application of the force (not after) should it only rotate around its instantaneous center of rotation (also called pole or center of oscillation/percussion)? Or it can also be subjected to...

When calculating the center of mass for an MD simulation, I've seen a few codes that subtract the average velocity from each atoms velocity. I think the reasoning behind this is that you want the velocity of center of mass for the simulation to be zero, which I understand, but I don't understand...

A rod of mass M (=4m) and length L is placed over a smooth horizontal table. One end of rod is attached with a block of mass m through a light string as shown in the figure. The pulley is friction less and light. the acceleration of com of rod at the given instant is (g = acceleration due to...

Homework Statement Homework EquationsThe Attempt at a SolutionMagnetic field due to both semi - infinite straight wires on P = Magnetic field due to infinite straight wire on P = ## \frac { \mu_0 I } { 2 \pi a } = 2 * 10 ^{-5} ~wb/m^2 ## Magnetic field due to semi – circular wire on...

Homework Statement Two equal 1 kg masses are connected by a light 1.6 m string on a flat frictionless surface. A 2 N force is applied to the midpoint of the string which causes the system to accelerate in the positive x-direction. After 1.5 seconds, the rope makes an angle of 55° with the...

Hello everyone, According to Archimedes' principle, a solid body immersed in fluid (gas or liquid) always experiences a net upward buoyant force due to pressure variations occurring within he hosting fluid. Pressure calculations show that the buoyant force magnitude is equal to the magnitude...

Homework Statement Consider the center of mass system of two interacting fermions with spin 1/2. a) What is the consequence of the Pauli exclusion principle on the two-particle wave function? b)Let S1 and S2 be the spin operators of the two individual fermions. Show that the operators...

I was just in a conversation with someone regarding the magnetic field resulting outside of a solid cylinder, with a current moving down the center of the cylinder, and then the resulting magnetic field after removing the current. Now I haven't thought about magnetic fields/magnets for a while...

Determine the center and radius of circle.

A. Determine the center and radius of circle. B. Also, find the y-coordinates of the points (if any) where the circle intersects the y-axis.

Hello, I am reading a review on weak gravitational lensing (https://arxiv.org/pdf/astro-ph/0509252.pdf) and they define the center of an image as follows: $$\vec \theta_c = \frac{\int d^2 \theta I(\vec \theta) q_I [I(\vec \theta)] \vec \theta}{\int d^2 \theta I(\theta) q_I[I(\vec \theta)]}$$...

Homework Statement Find the exact magnetic field a distance z above the center of a square loop of side w, carrying a current I. Verify that it reduces to the field of a dipole, with the appropriate dipole moment, when z >> w. Homework Equations (1) dB = μ0I/4πr2 dl × rhat (2) r =...

1. The problem statement, all variables, and given/known data A square of side 2 L is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C’. The displacement of the y coordinate of the center of mass (from...

Dear Everybody, Shown below is a 4.00-ft by 8.00-ft sheet of plywood with the upper left quadrant removed. Assume the plywood is uniform and determine the x and y coordinates of the center of gravity. Hint: The Earth's gravitational field is also uniform for the entire sheet of plywood. I...

Hello everyone, I know that the any object, human body included, when the vertical line from its center of mass to the floor falls outside the base of support, topples under the influence of gravity: the force of gravity produces a nonzero torque that rotates the body. Is the human body able to...

Homework Statement Find the z -coordinate of the center of mass of the first octant of a sphere of radius R centered at the origin. Assume that the sphere has a uniform density. Homework Equations Mass = Integral of the density function Center of mass for z = Integral of density * z divided...

dear physicists is it possible to download full data of half lives (or another parameters) from Chart of Nuclides in http://www.nndc.bnl.gov/chart/ I can see data One by one for extract my Required data and it is too time consuming So, if there's any way I can download all the information, it...

PICTURE INCLUDED 1. Homework Statement A piece of wire is bent into an isosceles right triangle whose shorter sides have length a The wire carries current I. Calculate the magnetic field for point P. Point P is located on the Y-axis ( 0, √2a). Two corners of the triangle are are located at...

Homework Statement A solid B occupies the region of space above ##z=0## and between the spheres ##x^2 + y^2 + z^2 = 16## and ##x^2+y^2+(z-1^2) = 1##. The density of B is equal to the distance from its base, which is ##z = 0##. The mass of the solid B is ##\frac{188\pi}{3}##. Find the...

I have a baseband signal in IQ form. I have a method to calculate the carrier offset and estimate the carrier bin. I want to center the carrier to the middle of the bandwidth. How do I do so? Do I simply multiply the IQ data by the exponential with the carrier offset, but doesn't that shift the...

$\tiny{232.15.6.31}$ $\textsf{Find the center of mass of the following solid, assuming a constant density.}$ $\textsf{Sketch the region indicate the location of the centriods}$ $\textsf{Use symetry when possible and choose a convient }$ $\textsf{coordinate system the sliced solid cylinder...

How can I understand logically this equations? it seems to me like an avarage of equation...but why each term is specifically in the way it is? Thank you

Homework Statement Suppose I have particles with masses m1 and m2 , both are in freefall: Then , looking at the center of mass coordinates , I know that the sum of momentums of masses m1 and m2 in the center of mass coordinates is equal to zero : P1c + P2c = 0 so now I know that the total...

In reading Jules Verne's book A Journey to the Center of the Earth I came to a section where one of the characters questions if the massive weight of the air would be fatal at the center of the Earth. I lack the mathematical skills to derive an equation to graphically represent the results. My...

Homework Statement A cubical block of ice of mass m and edge L is placed in a large tray of mass M. If the ice melts, how far does the center of mass of the system "ice plus tray" come down ? Homework EquationsThe Attempt at a Solution What I thought was that if no net force is acting on the...

Homework Statement Consider a glass sphere completely filled with water except for a small air bubble at 1 atmosphere. The sphere is accelerating to the right. What is the pressure at the center of the sphere? Let Pe = Atmospheric pressure r = radius of sphere pw = density of water a =...

$\newcommand{\un}[1]{\,\text{#1}}$ https://www.youtube.com/watch?v=xSVHWiZu8NM One of my relatives sent me a link to a video (above) claiming that the WTC towers must have had internal demolition in order to fall as fast as they did. I think there are good reasons to oppose the theory, but I...

told so in another thread that two photons traveling in opposite directions "have mass". I understood the concept of centre of momentum, an inertial frame of reference and rest mass. My cynical reply wasn't conveyed and I got well thought out and accurate replies. the COM is an idealized point...

1. The problem statement, aall variables, and given/known data I need to find the angle between a point on the ellipse and the ellipse's center shown in the figure below: The known variables are 'd', the distance between point O (the center of the ellipse) and point A, and 'a', the angle...

Violet itself is weird, because it lays at the other side of the spectrum than red, yet it can be easily mimicked with red and blue. The more powerful the violet light, the more it resembles white. My hypothesis: Violet tricks our eyes by activating not only blue, but also red and... with more...

I was doing some practice problems to become more familiar with the Center of Mass Velocity and I came across this one from (Noted in the picture) Engineering at Illinois, that relates the velocity of the center of mass in both the x and y direction, however I don't quit understand the answer...

My creationist grandpa says that we are at the center of the universe and that other galaxies are in spherical shells around us and claim that this means we are in a special place in the universe. Basically he believes in the "quantized redshifts" thing you may or may not have heard of, which...

Can someone clarify this for me-- how is the motion of the center of mass unaffected by internal forces, as is stated towards the end of the paragraph in the picture I've provided. It seems to me that motion of the center of mass directly affected by these internal forces. Specifically, the...

Homework Statement Consider a conductor wire with a charge Q uniformly distributed, shaped in the form of an arc of radius R and amplitude 2A (were A is a given number between 0 and π). Find the value of the electric field in the center of the arc. Homework Equations ##E(P)= \int K_e...

Homework Statement Find the coordinates for the center of mass in the picture above. Plate is uniform.Homework Equations Since it's uniform, the lengths can be converted to the mass. So: coord x =(M1X1 +M2X2 + M3X3 + ... +MiXi)/(M1 +M2 + M3 + ... +Mi) coord y =(M1Y1 +M2Y2 + M3Y3 + ...

I have a question for the community. I am doing a further study and trying to locate any information regarding input impedance of an off center fed dipole at different heights above ground. A simple dipole targets 73.1 ohms for 1 wave length or higher above ground. I am not sure if the same...

Homework Statement [/B] Find the radius and center of sphere ρ = 28 cos ϕ. Homework Equations Relevant equations would be the spherical and rectangular coordinate equations. The Attempt at a Solution I started off by multiplying both sides of the equation by ρ to get ρ^2 = 28 ρ cosϕ Then...

Supposing that we have a hollow sphere of mass m and radius R. Furthermore, suppose that we attach the sphere to a rod of length L and mass M. Now, suppose we rest the rod-sphere contraption on a pyramid a distance (X+R) from the center of mass of the sphere and a distance [(L/2)-X)] from the...

So a few months or years ago I learned that most of the energy from swinging comes from raising the center of mass at the lowest point of a swing. I also recently found a method of swinging that maximizes this energy gain. You squat on the swing, and stand up every time it gets to the lowest...

Homework Statement Three identical rectangular blocks are at rest on a level, frictionless surface. Forces of equal magnitude that act in the same direction are exerted on each of the three blocks. Each force is exerted at a different point on the block (indicated by the symbol "x"), as shown...

Hello. The following situation I thought out confuses me so I am wondering where my mistake lies. A uniform disk of mass M and radius R sits on its edge. A string is attached to the highest point and pulled with a Force F in the x direction. The moment of inertia of the disk is MR^2/2 making...

I was passing time by Googling the properties of the sun (temperature, mass, etc) and got to wondering what lies at the center of stars. I found out its plasma under roughly 340 billion atmospheres of pressure. I realize Boyles law may not be strictly meant for plasmas, but using it I...

Find the mass and center of mass given the following region R. R: triangle with vertices (0,0), (b/2, h), (b,0) Let p = rho p = k The letters b and h as given in the points make it hard to find the equation of the lines needed for the inner upper and lower limits. I have worked this out...

Find the mass and center of mass of the lamina bounded by the graphs of the equations for the indicated density. y = sqrt{a^2 - x^2}, y = 0 Rho = k 1. How do I find the inner and outer limits of integration? 2. Is k the density function? 3. Is the letter a in the radicand constant? 4. Is...

Find the mass and center of mass of the lamina for the indicated density. R: (0, 0), (a, 0), (0, b), (a, b) ρ = k I know the formula to find the mass and center of mass. My problem is twofold: 1. Finding the limits of integration for the inner and outer integrals considering the fact that...

In simple terms, what exactly is the center of mass as taught in Calculus 3?

Homework Statement A cube of mass M rests tilted against the wall as shown (see below). There is no friction between the wall and the cube, but the friction between the cube and the floor is just sufficient to keep the cube from slipping. When ##0\lt\theta\lt 45^\circ## find the minimum...

Hi, in terms of oblique collisions, COM frames and laboratory frames, is this statements ALWAYS true? "The scattering angle of the first particle in the laboratory frame is half of the scattering angle in the center of mass frame." Please elaborate if you know, thanks in advance!

Homework Statement "Represent (linear) acceleration of center of mass of link OA in terms of variables shown." OmegaOA is given to be some constant value, I have assigned it 'omegaOA'. Homework Equations Already derived equations to previous parts of the problem, fairly certain these are...

I have a model of two slender rods (call them OA and AB) connected with a pin at A, anchored at O with a pin, and attached to horizontal slider at B. I am supposed to show graphs of different variables in Matlab as the angle theta changes. One of these steps is to show the acceleration of the...