Center Definition and 1000 Threads

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...

Homework Statement Find teh center of mass of a thin infinite refion in the first quadrant bounded by the coordinate axes and the curve y=e-2x, if ρ(density)= xy Homework Equations The Attempt at a Solution I set M= ∫∫ xy dydx where y goes from 0 to y=e-2x, and x goes from 0 to...

Homework Statement Let m1, m2 and m3, the mass of 3 particles and v12, v23, v13 their respective relative velocities. a) Show that the total kinetic energy of the system in relation to the center of mass is: ( m1m2v12^2 + m2m3v23^2 + m1m3v13^2 ) / (m1+m2+m3) b) generalize this result...

Suppose I give you a curve f(x) = \sin^2 (x) + ln(x) And suppose I tell you to rotate this curve about the x axis, we get disks. Now, I ask you, what is the center of mass of this object? Now immediately, you could say that \bar{y} = 0 because it is symmetric about the x-axis. I don't...

Homework Statement Find the center of mass of a triangle with two equal sides of length a. The triangle's third side is length b and it has a uniform mass of M. Homework Equations R = \frac{1}{M} \int dm \vec{r} dm = \frac{M}{A} A = \frac{1}{2}base*height The Attempt at a Solution...

Homework Statement I have to find the velocity of center of mass of a elastic collision. Momentum: Ball Ai = .23 J Ball Af = .06 J Ball Bi = .02 J Ball Bf = .19 J Am I correct in saying that all you have to do is you take the total momentum of both balls and divide by the...

Homework Statement Hey all. Below is the question and picture related to it. "Three uniform metre sticks each of mass M are attached together as follows: Stick 1 lies along the y-axis from y = 0 to y = 1.0m. Stick 2 lies along the x-axis from x = 0 to x = 1.0m. Stick 3 makes an angle of 60...

Velocity and Center of mass question? Homework Statement Having some issues with this one. "Ball A has a mass of .200kg and a velocity of 1.50 m/s. Ball B has a mass of .300kg and a celocity of -0.400 m/s. The balls meet in a head on collision. After the collision, the velocity of ball...

Which is the correct formula to calculate the center distance between gears? I am designing a couple of spur gears in Autodesk Inventor and the application says that the center distance between them is 23.107 mm, but when I place them so far apart they seem to overlap. The gears have the...

On a horizontal air track, a glider of mass m carries a post shaped like an inverted "L". The post supports a small dense sphere, also of mass m, hanging just above the top of the glider on a cord of length L. The glider and sphere are initially at rest with the cord vertical. A constant...

Homework Statement Let D be the upper half of the disc x2+y2 ≤1(that is, the part of the disc with y ≥ 0). Suppose the lamina Ω fills the region D, and has density given by ρ(x, y) = |x|. (a) Calculate the mass of the lamina. (b) Find the coordinates of the center of mass of the lamina...

Homework Statement A person with mass m1 = 69 kg stands at the left end of a uniform beam with mass m2 = 108 kg and a length L = 2.5 m. Another person with mass m3 = 67 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 9 kg (assume that the medicine ball is at...

In a recent thread, it is stated that the universe did not start its expansion in a ballistic type event, and it did not expand from a center. Could someone please describe how these things could be so.

Homework Statement Set up intergral expression for center of mass of a cone using cylindrical coordinates with a given height H and radius R Homework Equations rdrddθdz is part of the inter grand. M/V=D volume of cone is 1/3π(r^2)H The Attempt at a Solution dm=Kdv dv=drdθdx K...

Homework Statement In the 1968 Olympic Games, University of Oregon jumper Dick Fosbury introduced a new technique of high jumping called the "Fosbury flop." It contributed to raising the world record by about 30 cm and is presently used by nearly every world-class jumper. In this technique...

Im trying to figure out the center of mass of a cone for this research I'm doing. How do I find the center of mass of a cone?

Homework Statement Three ice skaters are on a perfectly smooth frictionless lake. They are together at rest at the middle of the lake when they push off on each other. When skater #1 (m1 = 80 kg) is 6.00 meters EAST of the starting position, and skater #2 (m2 = 60 kg) is 6.00 meters NORTH of...

Find the x and y coordinates of the center of mass of a flat triangular plate of a height H =17.3cm and a base B = 10 Cm Homework Equations Area = A = 1/2bh x = 1/A ∫ x(f(x)) y = 1/A ∫ 1/2((f(x)^2) The Attempt at a Solution Area = 1/2(10)(17.3) = 86.5 f(x) = 17.3-1.73x or...

1. A bumper car with mass m1 = 105 kg is moving to the right with a velocity of v1 = 4 m/s. A second bumper car with mass m2 = 98 kg is moving to the left with a velocity of v2 = -3.8 m/s. The two cars have an elastic collision. Assume the surface is frictionless. 2.Vcm= (m1v1+m2v2)/m1+m2 V1 in...

My understanding is that if for example one object is orbiting another, then the mass center of the two masses is located somewhere in between the two objects. And if we have many object (for example stars), then the mass center of the total system can be located another place than were any star...

Figure 12-52a shows a horizontal uniform beam of mass mb and length L that is supported on the left by a hinge attached to a wall and on the right by a cable at angle θ with the horizontal. A package of mass mp is positioned on the beam at a distance x from the left end. The total mass is mb +...

A solid uniform disk of mass 19.0 kg and radius 70.0 cm (.7 m) is at rest FLAT on a frictionless surface. A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim. The string is being pulled. When the disk has...

Homework Statement A very massive object with a velocity "v" collides head-on with an object at rest whose mass is very small. no kinetic energy is converted into other forms. Prove that the low-mass object recoils with a velocity 2"v" use the center-of-mass frame of reference...

I have been thinking about how to come up with a function of time for the n-body problem. Later I found that there still is no function of time known for the n-body problem, but I am still not sure where the brick wall for everyone is because I am quite sure my understanding has hit from very...

Homework Statement find center of mass Homework Equations (r1m1+r2m2+...)/m1+m2+...The Attempt at a Solution cut into two pieces with one center at 2,5 and one 3,2. used each square on grid as one unit is that okay?

If someone is on a boat that rests in a placid river with negligible friction between the boat and the river ,, suppose that person moves a certain distance ,Does that boat move as well , if so why ?

A small square plank of oak floats in a beaker half full of water. The piece of oak is 7 cm on a side and 3 cm thick and floats on its side as shown in Figure P10.80. Density of oak 750kg/m^3 Density of water 1000kg/m^3 There were two parts to the problem, the first is: Find the location of the...

Homework Statement Let G be a finite p-group, where p is a positive prime. Show that G has nontrivial center. In other words Z(G) \neq {e}. The Attempt at a Solution So the centre is pretty much the "abelian subgroup" of G, or all the elements that commute with every other element. Now I...

Homework Statement A 1000 kg horse trailer with frictionless wheels is sitting in a level parking lot. The trailer is 4 m long, and its center of mass is at its center. Its passenger, a 500 kg horse, breaks free from its stall at one end of the trailer and walks to the other end. How far...

[Edit: ignore the below I realized what it represented later this afternoon. Probably because I asked and stopped thinking about it.] Jack is at the top of a hill that is 35 degrees. Jill is at the bottom of the hill on another slope which is 22 degrees. Determine the acceleration of the center...

Let p be a positive constant. Suppose that a random variable X has probability function f(x)=cxp(1-x) for 0≤x≤1. Find formulas for c, μx, and Var(X) in terms of p. I know Var(X)=∫(x-μx)2f(x)dx I know that I did not show any work so please just give me a hint (I'm not asking you to solve...

How can one calculate the center of mass of a system made of two photons? I know that they have zero rest mass so the first intuition is to say that they do not have any center of mass. However, I read about something called center of momentum which is defined as a frame in which a moving...

We have a sphere that its center of mass is not located in its center. suppose it has a mass of m. what we want to do here is to write its movement equations, using Newton's laws or lagranigian.by move ment we mean writing the equations if a) a force F acts on the body on a surface that is...

Homework Statement [PLAIN]http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam2/sp10/fig3.gif A 4.0 kg circular disk slides in the x-direction on a frictionless horizontal surface with a speed of 5.0 m/s. It collides with an identical disk that is...

Hi ! Somewhere I read about our solar system is going slowly out of our galaxy (moving backward from the center, but then I can also read our solar system is approaching center with sonic speed. So how is our solar system actually moving toward the centre of milky way (beside rotation around...

Homework Statement An amonia NH3 molecule in the figure has three hydrogen atoms, which form a equilateral triangle as the base of a pyramid. At the top of the pyramid is the nitrogen atom. The length between any two hydrogen atoms is 9.4x10^-11, the length from nitrogen to any of the...

I am a bit confused about a statement I read in my textbook saying the sum of external forces on a body is equal to the body's mass times the acceleration of it's center of mass. It seems to me if a long rod is suspended in the air by a string at its center of mass, and I tap the rod near one of...