Center Definition and 1000 Threads

<Mentor's note: ^Moved from a technical forum and therefore no template.> at the instant shown during deceleration, the velocity of the tire is 40 ft/s to the right and the velocity of point A is 5ft/s to the right. locate the instantenous center of rotation. Can the instantaneous center of...

Homework Statement A 45 RPM record is a disk with a wide hole in the center. The mass of such record is 45g. It is 7 inches in diameter, and the hole in the center has a 1.5 inch diameter. (Sorry for the odd units, this was the way it was given). Find the moment of inertia of the 45 RPM...

Hello. The problem is this, what happens to angular momentum, tangential velocity and centripetal force when you change the center of rotation. For example, if we have rotating hinged arm, weight at the end, with certain angular momentum and tangential speed etc. which then gets stopped at...

Determine the center and the radius of circle. x^2 + y^2 - 10x + 2y + 17 = 0 Can this be done using completing the square?

An acquaintance has told me that the Sloan Digital Sky Survey found clusters of galaxies in which most of the galaxies were divided between the center and the periphery, with a smaller density of galaxies in between. Is this case, and if so, why?

Problem A 60kg woman walking at a speed of 1.0 m/s steps onto a long plank that has a mass of 60kg. Upon stepping on the plank, both she and the plank begin to slide with speed v and spin with angular rate ω on a frictionless surface. 1. How far from the woman is the center of mass of the woman...

Homework Statement On Earth, seasons occur due to the tilt of our planet. In the SSDS (A Dyson Sphere built around our sun), we can cause seasons to occur by having the Dyson sphere be not perfectly centered around the sun. If you want the sun to be 10% closer to the one side of the Dyson...

I am unsure on what exactly is at the center of the galaxy. I looked up some articles but some stated that scientists are unsure.

Homework Statement While not explicitly a homework question, I am having some trouble with deriving expressions for the center of mass energy in a fixed target experiment versus a collider experiment. The question is effectively, "Derive an expression for the center of mass energy in a fixed...

If the big bang through matter in every direction away from itself (the center) shouldn't there be a huge void there?

Why the center of Newton's ring is dark? though I am thinking the path difference in the center is zero between two reflected rays... so,I will be glad if you give the correct information about that...

Homework Statement A solid conducting sphere of radius R and carrying charge +q is embedded in an electrically neutral nonconducting spherical shell of inner radius R and outer radius 9 R . The material of which the shell is made has a dielectric constant of 2.0. Relative to a potential of zero...

Homework Statement What is the electric field at the center of a hemisphere bounded by r=a, 0<θ<pi/2 / and 0<∅< 2pi with a uniform surface charge density? Homework Equations (1/4piε0) ∫ p(r') ((r-r')/[r-r']^3) dr' The Attempt at a Solution Forgive my formatting ds= (r^2)sinθdθd∅ (In direction...

Homework Statement A baseball rests on a frictionless, horizontal surface. The bat has a length of 0.900m, a mas of 0.800kg, and its center of mass is 0.600m from the handle end of the bat (see figure below). The moment of inertia of the bat about its center of mass is 0.0530 kg.m^2. The bat is...

$\tiny{231.13.3.75}$ $\textsf{Imagine $3$ unit spheres (radius equal to 1) }$ $\textsf{with centers at, $o(0,0,0)$, $p(\sqrt{3},-1,0)$ and $q(\sqrt{3},1,0)$.} \\$ $\textsf{Now place another unit sphere symmetrically on top of these spheres with its center at R.} \\$ $\textsf{a Find the center...

Homework Statement 1. Show that for an arbitrary uniform triangle ABC, with A at (x1, y1), B at (x2,y2), C at (x3, y3), the CM (xcm, ycm), is simply defined by xcm=(x1+x2+x3)/3, and ycm =(y1+y2+y3)/3 Homework Equations xcm = 1/M * ∫xdm ycm = 1/M * ∫ydm M = ∫dm = ∫δdA where δ = M/A = dm/dA...

Homework Statement A Hydrogen atom is interacting with an EM plane wave with vector potential $$\bar A(r,t)=A_0\hat e e^{i(\bar k \cdot \bar r -\omega t)} + c.c.$$ The perurbation to the Hamiltonian can be written considering the proton and electron separately as...

In the figure , we can notice that the moment due to Pe is counterclokwise , but moment due to shear flow is also counterclockwise , How can the Pe prevent the twisting of the beam ? Or is the direction of the shear flow wrong ? Should it flow from the below to the top ?

I am a little bit confused on Center of Mass and Center of Gravity about what are they vectors or scalars . As I may think they are neither because they are simply two points . Am I saying right or wrong .

Hi all, I've been stuck on thinking about a situation where a mass splits in two in midair. The mass originally undergoes a projectile motion with no air resistance, and it splits in two in midair but one of the piece reaches the ground before the other. In this case, I know that the trajectory...

Homework Statement A small pine tree has a mass of 15kg. Its center of mass is located at .72m from the ground. Its trunk is sawed through at ground level, causing the tree to fall, with the severed trunk acting as the pivot point. At the instant the falling tree makes a 17° angle with the...

Suppose we have a rigid body that rotates around a point P other than its center of mass, with point P being a point of the rigid body. This implies that there are external forces to the rigid body. If the external forces cease to exist(like we have an axis passing through P and we suddenly...

I'm having a little trouble starting on this problem. Can someone help? I was trying to solve it out, but I just ended up telling how to draw the center. Attached is the problem:

Homework Statement One way of moving a large undersea rock or mooring is to fasten a closed, empty oil drum to the rock while at low tide. As the tide comes in the drum is drawn down into the water increasing the buoyant foce acting on the system of the rock and drum. Suppose a cylindrical drum...

In the notes , the author stated that when the force is applied through the centorid of cross section , the channel will bend and twist. but , on the second page , the author stated that the shear center lies on an axis of symmetry of member's cross sectional area... So, i am confused whether...

Homework Statement in the first photo , it's stated that the dy/dx at center = 0 , however , in the second photo (website) , it's stated that the dy/dx at the boundary = 0 ,which is correct ? I'm confused now http://www.geom.uiuc.edu/education/calc-init/static-beam/support.html Homework...

Homework Statement In the notes , the author stated that when the force is applied through the centorid of cross section , the channel will bend and twist. but , on the second page , the author stated that the shear center lies on an axis of symmetry of member's cross sectional area... So, i am...

Homework Statement Consider the planar quadrilateral with vertices (0, 0), (2, 0), (1, 1) and (0, 1). Suppose that it has constant density. What is its center of mass? Homework EquationsThe Attempt at a Solution Since it has constant density, could I assume that the center of mass would be the...

Homework Statement Two 0.50-kg carts are pushed toward each other from starting positions at either end of a 6.0-m low-friction track. Each cart is pushed with a force of 2.9 N , and that force is exerted for a distance of 1.0 m. What is the kinetic energy of the center of mass of the system...

Homework Statement A horizontal pole is made of 8 pieces, 1 meter apart each. Forces that do not act at the ends are shown in the picture. The pole does not rotate, and weighs 20N. a. What is the sum of forces applied on the pole? b. Where is it applied? c. What are the forces at the ends...

Homework Statement Water skiers often ride to one side of the center line of a boat, as shown in the figure (Figure 1) . In this case, the ski boat is traveling at 15 m/s and the tension in the rope is 90 N.If the boat does 3700 N of work on the skier in 54.8 m, what is the angle θ between the...

Homework Statement Find the center of mass of an inverted cone of height 1.5 m, if the cone's density at the point (x, y) is ρ(y)=y2 kg/m. Homework Equations The formula given for this problem is rcm=1/M * ∫rdm, where M is total mass, r is position, and m is mass. The Attempt at a Solution...

Homework Statement A long copper rod 8 cm in diameter has an off-center cylindrical hole 4 cm in diameter down its full length. This conductor carries a current of 900 amps flowing in the direction “into the paper.” What is the direction, and strength in tesla, of the magnetic field at the...

Homework Statement A solid sphere of density ##ρ## and radius ##R## is centered at the origin. It has a spherical cavity in it that is of radius ##R/4## and which is centered at ##(R/2, 0, 0)##, i.e. a small sphere of material has been removed from the large sphere. What is the the center of...

Homework Statement All three disks are made of sheet metal of the same material, and the diameters are 1.0 m , 2.0 m , and3.0 m . Assume that the x-axis has its origin at the left-most point of the left-most object and it points to the right. Part A) Determine the location of the center of mass...

"The weight of an exercise book in picture A (where the centre of gravity is not on the axis of rotation) rotates so it moves towards the second position in picture B (where the axis of rotation goes through the centre of gravity). Explain why." I don't believe any equations are necessary for...

Homework Statement An 8.0-kg object is sliding across the ice at 2.34 m/s in the positive x direction. An internal explosion occurs, splitting the object into two equal chunks and adding 16 J of kinetic energy to system. The explosive separation takes place over a 0.16-s time interval. Assume...

My name is Jackson Richter. I am retired from Rockwell-Collins and worked in the engineering lab for 31 years. Since my retirement my interested have peaked in radio communications. Especially in antenna design. Thanks to anyone here that would give me a little more insight with my...

Let BCED and ACFG square. Prove that center of DG = center of the red circle. I don't know how to start

Homework Statement Homework Equations triple integrals, center of mass The Attempt at a Solution I set up the triple integral x: lower limit 0 upper limit 1 y: lower limit 0 upper limit 2 z: lower limit 0 upper limit 1 ∫∫∫ δ(x,y,z) dx dy dz => applied the limits for x, y and z, and...

theoretically if you were in the center of the earth, would you age slower or faster from time dilation? this question is asked here as well: https://www.quora.com/Can-someone-calculate-the-time-dilation-if-you-were-in-a-5000-km-deep-cave-How-much-longer-would-my-life-be this is a wrong...

Homework Statement For the curve with equation y={ x }^{ 2 } at the point (1, 1) find the curvature, the radius of curvature, the equation of the normal line, the center of the circle of curvature, and the circle of curvature. Homework EquationsThe Attempt at a Solution \kappa \left( 1 \right)...

If the Earth were hollow and we only had the shell could a black hole at the center take the place of all the mass and provide us with gravity to keep us from floating away?

I've been wondering how all the stars of the Milky Way orbit the center of the Milky Way almost like it orbits Sagittarius A*. It is possible that there is a common center of mass that happens to be in the center of the Milky Way that also happens to be in the center, ultimately giving it its...

They just lost a rocket: http://www.bbc.com/news/world-us-canada-37247077']SpaceX[/PLAIN] rocket: Explosion at Kennedy Space Center ahead of launch http://www.bbc.com/news/world-us-canada-37247077'][/PLAIN]

Size O.D. Wall 3" x 2" x 0.1875 3" x 2" x 0.125 5ft long center 500lb how much bend will there be thank you for your time

On page 252 of Kleppner's Introduction to Mechanics (2d. Ed.) in Example 7.5, Kleppner analyzes the forces and torques on a uniform rod that have been bent into a quarter-circle of radius R and length PI*R/2. His diagram is attached. Kleppner writes, "[t]he center of mass is halfway along the...

You have an infinitesimally small mass in the center of octahedron. Mass is connected with 6 different springs (k_1, k_2, ... k_6) to corners of octahedron. Equilibrium position is in the center, you don't take into account gravity, only springs. Find normal modes and frequencies. Relevant...

I used to know this back when i worked with Flash animation, but I'm working on a 3D printer now and I've forgotten, when you have a set of teeth, on a linear shaft and a gear, do you base the unrolling of the gear, for the spacing, on the inside of the teeth, the outside of the teeth, or the...

Homework Statement Where are the instantaneous centers of rotation? Instantaneous center of rotation = 1. Velocity is 0 in this point. 2. This can be also a point where 2 parts "touch" each other and have the same velocity in this point. Homework Equations / The Attempt at a Solution...