Center of mass Definition and 900 Threads

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 A canoe of mass 38 kg lies at rest in still water. A man and a woman are at opposite ends of the canoe 4.0 m apart and symmetrically located with respect to the canoe’s centre (which is also its centre of mass). The mass of the man is 65 kg and the woman’s mass is smaller...

Homework Statement T is the solid bounded by the cylinder y^2+z^2=4 and the planes x=0 and x=3. The mass density at a point P of T is directly proportional to the distance between P and the yz-plane. Find the center of mass of the solid T. Homework Equations y^2+z^2=4 x=0 x=3 The...

I have the following process: two ingoing particles, a photon hitting a nucleus, and two outgoing particles, the nucleus and a pion. I have computed |M|2 and the differential cross section in the center of mass frame dσ/dΩCM; I now have to go into the lab frame, where the nucleus is initially at...

Homework Statement Find the mass and the center of mass of the solid E with the given density function ρ(x,y,z). E is bounded by the parabolic cylinder z = 1 – y2 and the planes x + 4z = 4, x=0, and z=0; ρ(x,y,z) =6. m=? x=? y=? z=? Homework Equations z = 1 – y2 and the planes x...

two automobiles each of mass 1200kg traveling a the same direction. Speed of one automobile is 29.0 m/s and the other is 19 m/s. Regard these automobiles as a system of two particles. a)what is translational energy of center of mass? I found velocity at center of mass which is 24 m/s and...

a(n) proton (mass 1.67x10^-27 kg) of kenetic energy 1.58x10^-12 J is moving toward a(n) proton (mass 1.67x10^-27) at rest. what is the velocity of the center of mass of the system I used the equation k=1/2mv^2 -> sqrt(2k/m)=v sqrt(2*1.58x10^-12 /1.67x10^-27)=4.34x10^7

Figure below shows the shape of a nitric acid (HNO3)molecule and its dimensions. Treating the atoms as particles, findthe center of mass of this molecule. a)I know that xcm=m1x1+m2x1+.../Total mass. The total mass in this case is 63 but based on the picture I don't know which mass I should...

Homework Statement Three uniform thin rods, each of length L = 22 cm, form an inverted U. The vertical cords each have a mass of 14 grams. The horizontal rod has a mass of 42 grams. What are the x coordinate and y coordinate of the system's center of mass? Homework Equations xcom=...

So...I have two different homework problems. I'm not asking for answers to these problems! Just clarification. In problem one I am asked: A thin disk with diameter d rotates about an axis through its center with 0.260J of kinetic energy.What is the speed of a point on the rim? I use E = 1/2Iω2...

Suppose two friends, with masses m2 = 1.3 m1, are on a perfectly smooth, frictionless, frozen lake. They are both holding the end of a rope of length Lo . a. Find the position of the center of mass, in terms of Lo , from the smaller person. b. If the two pull half of the rope in such...

Homework Statement Homework Equations X_{T} = \frac{1}{m}\int_{K}^{} x dmThe Attempt at a Solution I have decided a) and I got the volume to be ∏ volume units. I need help with b). I try to use the formula and I get this: X_{T} = \frac{1}{\pi}\int_{K}^{} 3\pi x sin^2xcosx dx But I need help...

I have decided a) and I got the volume to be ∏ volume units. I need help with b). I would need to have the physics of the problem explained. Please help me explain the physics, so that I from it can understand how to solve b). :smile:

1. The coordinates of the center of mass for the extended object shown in the figure are (L/4, −L/5). What are the coordinates of m1? (Assume m1 = 7 kg, m2 = 3 kg, and m3 = 5 kg. Use any variable or symbol stated above as necessary.) 2. 3. I too the centroid cordinates and...

I remember seeing a way to do this, can someone link me to some relevant material or post a proof and equation? Thanks

1.Two particles lie on an x axis, particle 1 at x = 1 m and particle 2 at x = 2 m. If you gradually increase the mass of particle 1, what happens to the center of mass of the two-particle system? 2.If an external force acts on a system of several objects, can the external force change the net...

Center of gravity and Center of mass different?? I was developing a test for my students and always look for a difficult question as the only bonus question. I came across the question in the book, "When are center of gravity and center of mass different?". I thought about it before looking at...

Homework Statement Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is bounded by the parabolas y = x^2 and x = y^2; ρ(x, y) = 23√x Homework Equations m = \int\int_{D} ρ(x, y) dA x-bar = \int\int_{D} x*ρ(x, y) dA y-bar =...

Homework Statement Find the center of mass of a 5kg circle with a radius of 4m with a circle that has a radius of 2m cut out from it. Homework Equations The Attempt at a Solution To be completely honest, I do not know where to start. I do know how to find the center of mass when...

Homework Statement find the center of mass of a thin plate with constant density in the given region. region bounded by y-axis, x=y-y^3 ; 0<=y<=1Homework Equations x(bar) = (integral)(a to b) α(x) * x * (f(x) - g(x)) ---------------------------------- (integral)(a to...

Homework Statement Find the center of mass of a thin plate of constant density (δ covering the triangular region in this first quadrant between the circle x^2 + y^2 = 4 and the lines x=2 ; y=2. Homework Equations x^2 + y^2 = 4 and the lines x=2 ; y=2. The Attempt at a Solution...

Uniform semi circle of radius R whose diameter is on the x axis. Since it is uniform and symmetric on the x axis, x = 0. For y, we have $$ y_{cm} = \frac{\int y\sigma dA}{\frac{\pi R^2}{2}} $$ In polar, $dA = rdrd\phi$. So the integral becomes $$ \int_0^{\pi}\int_0^R y^2\sin\phi drd\phi $$ How...

How does one prove the center of mass of a two particle system lies on the line joining them? Would we do this by contradiction? Suppose on the contrary that the CM doesn't lie on the line joining the two particles. Where do I go from here though?

Why can the total force exerted on an object be taken as if a single force was applied on the center of mass? I think at most the total force must be the sum of tiny equal forces uniformly distributed. The mass must at most be uniformly distributed too. And this only matters when we start...

A car of mass m moving East at speed v (v << c no need to use relativity) collides with another car of mass 2 m moving North with speed 3v. a) What are the x and y components of the center of mass velocity of the system just before the collision? b) If the cars stick together during the...