Center Definition and 1000 Threads

I understand that the center of mass is a point which can be considered to contain all of an object's mass, for the purpose of calculations involving universal gravitation. I also understand that the center of mass of an object of uniform density is located at the centroid. In this case, I...

I am interested in the following scenario. Suppose that you have a composite system, e.g. ion, atom or whatever you want. This system will have internal degrees of freedom (d.o.f.), i.e. relative positions and momenta, and also center of mass d.o.f..What i am looking for is to find an...

We know,by symmetry,that the center of mass of a uniform sphere is at its center.So we expect the formula r_{com}=\frac{\int r \rho d\tau}{\int \rho d\tau} to give us zero for this case.So let's see: r_{com}=\frac{\int_0^{R} \int_0^{\pi}\int_0^{2\pi} r^3 \sin{\theta} d\phi d\theta...

Homework Statement part #1: A wooden block with m1 = 2.9kg is sliding across a frictionless surface in the −x direction at 4.5 m/s. A smaller wooden block with m2 = 1.1 kg block is traveling in the +x direction at 2.9 m/s. part #2: Now they make a head-on elastic collision. (This means that in...

Homework Statement A person with mass m1 = 50 kg stands at the left end of a uniform beam with mass m2 = 95 kg and a length L = 2.4 m. Another person with mass m3 = 60 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 14 kg (assume that the medicine ball is at...

Homework Statement A closed volume is bounded by conducting surfaces that are the n sides of a regular polyhedron (n = 4,6,8,...). The n surfaces are at different potentials Vi, i = 1,2,3,...,n. Prove that the potential at the center of the polyhedron is the average of the potential on the n...

Hello,, I'm reading about beams in mechanics of matrials. But I'm a bit stuck because of one thing that I either don't understand or just don't comply with! So, here's a picture from the book: picture 003 It says that the center of mass should be at 2/3 of the length.. I tried to...

A uniform log of length 2.33 m has a mass of 94.9 kg and is floating in water. Standing on this log is a 72.7-kg man, located 18.9 cm from one end. On the other end is his daughter (m = 26.1 kg), standing 1.15 m from the end. Find center of mass [b]2. m1r1+m2r2/(m1+m2)=R [b]3. I used...

A disc of radius r is spinning about its center in the horizontal plane with a constant angular speed w (omega). A bug walks along the radius of the spinning disc traveling from the center of the disc toward the edge. The bug maintains a constant speed v relative to the disc. (In other words...

Homework Statement http://img9.imageshack.us/img9/2866/siyx.png Uploaded with ImageShack.us Homework Equations Where is the COM of the figure? (width = 8, height = 8) The Attempt at a Solution area of triangle: 0.5(8*8) = 32 32 - (pi(0.52) - (2.5*1) - (2.5*0.5) = 27.4646 I...

Homework Statement A very long wire carrying a current I = 5.0 A is bent into a semi-circle with a diameter of 10 cm as shown in the figure. What is the magnitude of the magnetic field at the point P, halfway between the ends of the straight sections of wire and at the center of curvature of...

Homework Statement A point charge q is at the center of a spherical conducting shell of inner radius a and outer radius b. How much work would it take to remove the charge out to infinity? Homework Equations Potential, W = 1/2qV The Attempt at a Solution I am going at this in...

The angular momentum of a system of particles α = 1,2,3,...n can be written as the sum of the two angular momenta: \vec{L} = \vec{R} \times \vec{P} + \sum_{\alpha} \vec{r_{\alpha}}' x \vec{\rho_{\alpha}}' where the first term is the angular momentum of the center of mass with all mass M = Ʃ mα...

A boxcar of length 8.00 m and height 2.40 m is at rest on frictionless rails. The empty boxcar has a mass of 3750 kg. Inside the boxcar, located at the left end, is a tank containing 2450 kg of water. The tank is 2.00 m long and 2.40 m tall. The tank starts to leak, and the water fills the...

Homework Statement A stone is dropped at t = 0 s. A second stone, with a mass 2.00 times that of the first, is dropped from the same point at t = 0.220 s. Assuming that neither stone has yet reached the ground, how far from the release point is the centre-of-mass of the two stones at t...

If a beam of light is on a trajectory that is perfectly tangent to the event horizon of a black hole (or a little below tangent, allowing it to "dip" into the EH for a moment), is it possible that that photon could be pulled into a never ending orbit around the black hole? Or is the gravity too...

Homework Statement I got an answer as you can see in both pictures, but apparently it is wrong. What did I do? Homework Equations The Attempt at a Solution In this picture I found the y components of the electric field at C. Since the bottom 2 are the same i just doubled one of...

Based on http://en.wikipedia.org/wiki/Sagittarius_A* So "mid to late 2013" - almost the time, are there any new observations yet?

Homework Statement Given a disc of radius 'R' with a charge 'h' above the center of the disc, find the electric field on the charge.Homework Equations ##E = \frac{kQ}{d^2}##The Attempt at a Solution I can find the charge density from a ring then integrate over R: ##\sigma = \frac{Q}{A}##...

I read that scalar matrices are the center of the ring of matrices. How would I prove this? Tips are appreciated. It is already obvious that scalar matrices commute with all matrices, but the converse seems tricky. BiP

Homework Statement r=7sin(∅) find the center of the circle in Cartesian coordinates and the radius of the circle The Attempt at a Solution My math teacher is impossible to understand >.< and then the stupid homework is online and crap blah this class but I REALLY want to understand the material...

Hello, I'm reading Mathematical Methods in the physical sciences by Mary Boas and in it, she defines the center of mass of a body in 3 dimensions \int \overline {x}dM=\int xdM \int \overline {y}dM=\int ydM \int \overline {z}dM=\int zdM In standard undergraduate textbooks...

first i might be using magnetic potential incorrectly so please be nice when correcting me. i'm attempting to model the behavior of a magnetic compass when it is placed next to a ferrous piece of metal. basically the compass will point to the metal rather than north. my first simplification...

Homework Statement Two small particles of mass m1 and mass m2 attract each other with a force that varies with the inverse cube of their separation. At time t0, m1 has velocity v directed towards m2, which is at rest a distance d away. At time t1, the particles collide. How far does m1...

This question is about this video on YouTube, in which a bullet is fired vertically into the center of a wooden block from below, sending the block up into the air. Next, a bullet is fired vertically but off-center into a similar block from below, again causing the block to rise into the air...

Sorry if I am woefully uninformed, but I am really curious. What happens to time at the center of a black hole according to general relativity?

why the binary star revolving around center of mass ? could type 2 supernova ever had a stellar wind after explosion ?

Homework Statement An 800 g steel plate has the shape of the isosceles triangle shown in the figure. What are the x and y coordinates of the center of mass? https://www.physicsforums.com/attachment.php?attachmentid=13559&d=1208292919 Homework Equations x=1/M ∫ x dm [b]3. The...

Homework Statement A rod is 10 ft long and has a density that goes from 4 to 24 lb/ft. a) Find the mass. b) Find the center of mass. c) Find the moment of inertia through the center of mass. Homework Equations I = Ml^2 I = I(cm) + Md^2 (parallel axis theorem) The Attempt at...

so for the center of mass of an object.. x = (m1x1 + m2x2 + ...) / M total y = (m1y1 + m2y2 + ...) / M total how come in this equation the denominator is the total mass of the system? It seems like it would make more sense to have the denominator the total mass in whatever component you...

I want to know about the center of our galaxy, and every other galaxy by the way, I heard that the condensed matter and light comes from a Super massive black hole that 'aspires' everything around it & I want to know if it's true ( If we have proved it ) or is it just a suposition, & by the way...

Homework Statement Let C be a curve given by y = f(x). Let K be the curvature (K \ne 0) and let z = \frac{1+ f'(x_0)^2}{f''(x_0)}. Show that the coordinates ( \alpha , \beta ) of the center of curvature at P are ( \alpha , \beta ) = (x_0 -f'(x_0)z , y_0 + z) Homework Equations The...

Hello, I am trying to describe the concept of center of mass, and need some help with particulars: The center of mass can be thought of the balancing point of a body; it is the point where mass is "evenly distributed" with respect to this point, such that if you were to place the body in a...

Hello, can someone explain to me what is the difference between center mass acceleration and angular acceleration? If i have an uniform disk laying still, then i give it a force to make it spin while it stays put. The angular acceleration obviously has a number. What about the acceleration of...

Gravity moving toward the center of the Sun?? Ok can someone tell me if I am wrong in my understanding here (in a heated debate with a physics professor) : As you move from the surface of the sun to the center, does the force of gravity increase or decrease and why? The point I am trying to...

Hi all:we all know that a motorcyclist need to tilt his/her center of mass with the motorcycle when he is turning in order to balance the torque exerted on him.When he is tilted, gravity exert a torque on him that allows him to balance torque by centrifugal force about the point of contact with...

Homework Statement Homework Equations not sure The Attempt at a Solution I am not sure how to start this problem.

Why are centre of mass of all uniform symmetric bodies at there geometric centre? We know the following result: "Consider a system of point masses m1,m2,m3... located at co-ordinates (x1,y1,z1), (x2,y2,z2)...respectively. The centre of mass of this system of masses is a point whose co-ordinates...

I spent days trying to find this information on the internet, but i think i will never find it, so i came here looking someone who knows it. The Mystery is : Where is the Gravitational center of the Local SuperCluster (Also known as Virgo SuperCluster) ? Some Usefull information that i...

Homework Statement Homework Equations mgh=\frac{1}{2}mv^2+\frac{1}{2}Iω^2 The Attempt at a Solution I used conservation of energy, and found that the final velocity of the center of mass is independent of the object's mass, so in both cases: v=\sqrt{gh} . Therefore, the ratio is 1. However...

What exactly is center of mass, and how do I calculate in three dimensions? Also, I need to know how to calculate it in three dimensions at relativistically high speeds? Also, what do they mean by 'center of mass frame', as in the question "What are the energy and momentum in the center of...

I was doing some simple physics with a ball resting on a table and I made this curve (0,0) (25, 6.8) (50, 27.51) (75, 63.4) (100, 112.34) (125, 175.7) (150, 253.3) (175, 345.4) I was wondering if anyone could identify what sort of curve it is? I am just curious. This is not a homework...

Nowadays, Turkish police use water cannons and tear gas to disperse protesters. Local media is almost completely silent to this action. Thousands of people just using their democratic rights of protesting the destruction of a park in Taksim square. However, they are experiencing barbarous...

Homework Statement Locate the x coordinate of the center of mass of the homogeneous rod bent into the shape of a circular arc. Take r = 170 . The arc goes from (-5/6) to (5/6)pi (counterclockwise). It has a radius of 170mm.Homework Equations x=rcosθ, y=rsinθ, dL=r*dθThe Attempt at a Solution...

Homework Statement Locate the x coordinate of the center of mass of the homogeneous rod bent into the shape of a circular arc. Take r = 170 . The arc goes from (-5/6) to (5/6)pi (counterclockwise). It has a radius of 170mm.Homework Equations x=rcosθ, y=rsinθ, dL=r*dθThe Attempt at a Solution...

Hello, I am trying to find the angular velocity of a link in a 4 link mechanism problem but I have reached a scenario which is new to me. Please look at the attached image. I already know the velocity of the slider which is 3m/s. I have indicated in the diagram a line parallel to AB to indicate...

Hi to everybody Homework Statement I´ll show the problem with a picture: Homework Equations L\overline{x}=∫xc ρ dl The Attempt at a Solution Well the total length of the rod is 1 feet, I only need to calculate the integral. The moment xc of a differential element of mass of the rod is...

Homework Statement The boundary of a lamina consists of the semicircles y=\sqrt{1-x^{2}} and y=\sqrt{4-x^{2}} together with the portions of the x-axis that join them. Find the centre of mass of the lamina if the density at any point is proportion to its distance from the origin. Homework...

Homework Statement If the electric potential of the inner shell is 10 volts and that of outer shell is 5 volts, then the potential at the center will be? Homework Equations The radius of inner shell = a (given) The radius of outer shell = 2a (given) The Attempt at a Solution Having read...

Homework Statement A homogeneous ring lays horizontally on two identical parallel rails. The first rail moves parallel to itself, with a constant speed v; the second rail is at rest. The angular distance between the ring-rail contact points, as seen from the center of the ring, is 2α for the...