Center Definition and 1000 Threads

So my problem is this: I need to figure out the center of a circle given two points. At one of the points, I know the tangent angle. So I know (x1, y1, θ1) and (x2, y2) and need to find (xc, yc). I also need to do this on a computer so I need some sort of closed-form solution. The way I...

Textbooks all say that the center of gravity of an object is the point at which all it's gravitaional effects appear to be concentrated. But that seems to depend on who's checking. (see atachment) Imagine a small mass M some distance from the Earth. That mass is attracted simultaneously...

Hey, so I'm new to Physics Forums as a registered member, but I've been checking this site out for what seems likes years. Homework Statement Locate the center of the mass of the Earth-moon system with respect to the center of the Earth, and then find the orbital velocity of the Earth...

Text of the problem: Because the Earth rotates about its axis, a point on the equator experiences a centripetal acceleration of 0.033 7 m/s2, whereas a point at the poles experiences no centripetal acceleration. Assume the Earth is a uniform sphere and take g = 9.800 m/s2. (a) If a person at...

Homework Statement Show that the buoyant force on a partially submerged object acts at the center of gravity of the fluid before it is displaced. This point is called the center of buoyancy. The Attempt at a Solution I need to get better at proofs, so try not to just give me the...

Homework Statement A point charge is placed at each corner of a square with side length a . The charges all have the same magnitude . Two of the charges are positive and two are negative, as shown in the following figure. my figure: (image each charge represents a corner of the square)...

Homework Statement Calculate the electric field at the center of a square with side length .360 m. The charges, clockwise from top left on the corners, are Q1 = 4 x 10^-6, Q2 = 3 x 10^-6, Q3 = 1 X 10^-6 and Q4 = 5 x 10^-6 Coulombs. Homework Equations E = kq/r^2 where k = Coloumb's...

Hi all, How do I find the center of a circle given a point (tangent to the circle) and the radius. Thanks, CG

Hello all, I'm confused with the center of mass concept. Regard the following problem, we have a spring with negligible mass joined to two masses m1 and m2 (m1=m2) on a table without friction force. At t=0 a thrust Vo (initial velocity) is given to m2 with direction perpendicular to the...

A solid half-cylinder of radius 1 meters and length of 5 meters lies under 50 meters of water at the bottom of a lake. The cylinder is made of a material of constant density d. 1. Find the center of mass. I said that the COM will be in the center because there is a constant density. 2...

Homework Statement See attachment. Homework Equations The Attempt at a Solution I don't get the first equation. Why is it 2pALx on the left side? Aren't we finding the mass center of the second shorter body? So shouldn't it then be (5/2)pALx? On the right side, I know pAL(L/2) is...

Let's say a city planner plans to place a fountain that is equidistant from where people will want to walk toward a water fountain (e.g, where a runner will likely stop along a trail and turn towards a water fountain). He identifies 7 such spots. How would the builder go about finding the...

Homework Statement A uniform plank of length 5.0 m and weight 212 N rests horizontally on two supports, with d = 1.41 m of the plank hanging over the right support. To what distance, x, can a person who weighs 433 N walk on the overhanging part of the plank before it just begins to tip...

Hi I'm new to this forum. I've always wanted to know how much force it would take a person to escape the center of the earth. Let's say someone is buried deep into the Earth's mantle nearing the outer core. How much weight of rock (be specific if you can) would be upon that person's body and how...

Homework Statement Four masses are connected by 17.4 cm long, massless, rigid rods. If massA=105.0 g, massB=231.0 g, massC=204.0 g, and massD=248.0 g, what are the coordinates of the center of mass if the origin is located at mass A? See attached picture. Homework Equations Xc.m = \sumΔm x...

Homework Statement A point charge is placed at each corner of a square with side length a. The charges all have the same magnitude q. Two of the charges are positive and two are negative, as shown in the following figure. The two positive charges are on top and the two negative charges...

I am doing exercises from Hungerford's text 'Algebra', and would appreciate if someone took the time to verify my write-up for me, and possibly provide me with tips how this could be done more efficiently (using less mathematical machinery) Homework Statement If a normal subgroup N of order p...

So i read the answer of Marcus in the thread "Where is the Center of the Universe" where there was a brief mention of the "Un-Copernican" view of the Cosmos. Now i do not think that we are at the center of the Universe but this got me thinking. "IF" the homogeneity of the Cosmos really was...

Hello to everyone! I am really desparately trying to find the length of the "radius" of an ellipse.I will explain exactly what I mean by that - its the length of the line segment that connects the center of a particular ellipse with a given point of the same ellipse.All the information I have...

We know that the universe is expanding,but do we know from which point it is expanding outwards?

There must be a center or someplace close to the center of the universe. The actual universe can be contained in a physically describable bounding box. This box will have a center. Or, everything emminated from a center, the singularity and the position of that place where the singularity...

Hey all! I always use this principle when I do exercises, but today I found out, that I can't explain why it's valid. What I'm talking about is that when you apply a torque to a free object it will always start to rotate around it's center of mass rather than just an arbitrary point. Why is...

[SIZE="2"]Most posters on the subject of the center of the universe seem to believe that there is none. If the universe is indeed the consequence of a "singularity" or cosmic micro-pea that blew up about 14 billion years ago, the singularity or micropea once represented the center of what...

Six problems due Monday, and I have no idea what I'm doing on either of these. Problem 1: Homework Statement A group of people has a total mass of 1500kg and are standing on one end of a 20,000kg boat. They walk 6.5m to the other end of the boat. How much does the boat move? The water...

What is ceter of gravity concept and how to calculate it for a triangle

I am curious about time dilation of atomic clock positions on and in the Earth. If you had a long tube going through the Earth with one atomic clock on the surface of the Earth and one in the center of the Earth which would experience more proper time?

If we are not located at the center of the universe, then when we look out into space are we not sometimes looking towards the center of the universe and at other times towards maybe the edge of the universe. Assume the universe is finite- since we put an age on it, and the fact that it is...

Lets say I have n number of masses, x1, x2, x3,...,xn. How do I find the center of mass of the group of masses? I'm not really sure how to do this, but does it have something to do with having a test mass and finding the direction of the force and different points around the group of masses...

Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...

Homework Statement A uniform door(.81m wide and 2.1m high) weighs 140N and is hung on two hinges that fasten the long left side of the door to a vertical wall. The hinges are 2.1m apart. Assume that the lower hinge bears all the weight of the door. Find the magnitude and direction of the...

Homework Statement 1. Find of the center of mass of the image below. 2. A human head weighs 8lbs, a human torso weighs 20lbs, and a human's hips and legs weighs 20lb. The headis 10m long, the torso is 25m long, and the hips and legs are 35m long. Find the center of mass of the body...

Why is it that for instance the Earth and the moon orbit their common center of mass? I mean surely the moon feels a gravitational force as though the mass of the Earth were concentrated at its center? If yes, what is that then makes it orbit around their center of mass rather than this point. I...

Hey guys and gals, I'm not an electrical-anything so please forgive my lay-person speak. I work in a lab. One of our rooms has a high magnetic field. It is causing interference with some analytical and computer equipment. Of course there is some health concern as well... Half of this...

my textbook says: "As a gyroscope precesses, its center off mass moves in a circle with radius r in a horizontal plane. Its vertical component of acceleration is zero so the upward normal force exerted by the pivot must equal mg." Now wouldn't this always be true. I mean if u have a...

Homework Statement The ellipse 18x^2+2x+y^2=1 has its center at the point (b,c) where b=____ and c=____? Homework Equations x^2/a^2 + y^2/b^2 = 1 The Attempt at a Solution 18x^2+2x+y^2=1 18(x^2+(1/9)x)+y^2=1 18(x^2+(1/9)x+(1/324))+y^2= 1+18(1/324) 18(x+(1/18))^2+y^2=19/18...

From https://www.physicsforums.com/showthread.php?t=40391 in gravitational time dilation. At the center of neutron star PSR J1614-2230 at 1.97 SM mass of Sun 1.9891×10^30 kg mass of PSR J1614-2230. 4 ×10^30 gravitational constant = 6.67300 × 10-11 m3 kg-1 s-2 radius(rough estimate) =...

1. My professor explained this concept before, but I didn't quite understand. I need help with understanding how if two players jump for the ball with the exact same mass and body segment dimensions, taking off with the same vertical and horizontal velocity of the CoG, one can have an advantage...

Homework Statement Find the center of mass of figure , of uniform density Homework Equations X = m1 x1 + m2 x2 + ... / m1 + m2 ... The Attempt at a Solution i broke the figure in 4 rectangles and got individual center of masses my answers comes out to be (13b/8 , 5b/2)...

Hi there, i have a problem trying to derive the equation for the shear centre of a thin walled slit circular section of uniform section. I have attached a photo of the question bellow. it is taken from mechanics of materials. I hope someone can help.

Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...

Homework Statement mass of the mouse = 0.05 kg disc's radius = 0.2m disc's angular speed = 33 rev / min assume that the angular speed ω doesn't change Homework Equations tangential speed = ω * r The Attempt at a Solution well, what i did was: drew the vectors, one was the...

I am aware of the theorem |G/Z(G)|=p with p prime implies G/Z(G) is cyclic and thus G is abelian, but I do not understand why. Is there not a theorem that says G abelian \Leftrightarrow Z(G)=G? So what if |G|=p^{3} and |Z(G)|=p^{2}? This implies |G/Z(G)|=p implying G is abelian however...

Homework Statement a baton twirler throws a baton straight up in the air, it goes up and comes straight back down. it completes 4 rev. ignoring air resistance and assuming the angular speed is 1.80 rev/s , determine the height to which the center of the baton travels above the point of...

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 parabola x=y2 and the line y = x - 2; ρ(x, y)=3Homework Equations m=\int\intD ρ(x, y) dA The Attempt at a Solution Basically I just need help...

Homework Statement 1. Homework Statement On a frictionless table, a glob of clay of mass 0.72 kg strikes a bar of mass 1.34 kg perpendicularly at a point 0.23 m from the center of the bar and sticks to it. If the bar is 1.22 m long and the clay is moving at 8.3 m/s before striking the...

Homework Statement If a is the only element of order 2 in a group G, prove that a is an element of Z(G). [Z(G) is the notation used by the book for center of group G] Homework Equations Z(G)={a is an element of G: ag=ga for every g that is an element of G} The Attempt at a...

Homework Statement Given that I have a system with a rod of diameter 1 1/2 inches with a length of 17 in and a weight of 10 1/3 oz and a rod with a diameter of 3 inches with a length of 17 in and a weight of 20 2/3 oz. The two rods are butted together at one end almost looking like a bottle...

Given the picture in the attachment of two rods touching with them each being 17 inches long and one weighing double the weight of the other, would it make sense that the center of mass is 2/3 of the way down the picture from the thinner end? Or, am I going about this idea the wrong way?

I am currently trying to find the center of mass of two rods. One rod is 20 2/3 oz and is 17 inches long with a diameter of 3. The other rod is 10 1/3 oz and 17 inches long with a diameter of 1 1/2 The bigger rod is touching the smaller one if they were both standing up. It looks almost like a...

Homework Statement The upper side of a uniform plate of thickness w is given by a function y(x) = 4a+x^2/a. Length of this plate on the x-axis is a . Find x coord of the center of mass of this object, with respect to the origin O . Take density of the plate as p The Attempt at a Solution...