Center Definition and 1000 Threads

Homework Statement Two bodies with an equal mass of M are attached by a pole with no mass with a length of L. The system is placed on a horizontal table and at first it is at rest. At t=0 a bullet with a mass of m hits the pole, as described in the picture. The collision is completely elastic...

Hello, As many know, when an external force acts on a rigid body and the force's line of action does not pass through the body's center of mass ##c.m.##, the force will cause the body to both translate and rotate exactly about the ##c.m.##. Otherwise, the body will solely translate without...

Homework Statement Assuming you know the core mass, and other data about the sun, such as temperatures and pressures. Find the density at the very center of a star. Homework Equations I think this may be involved. P(r) = p(r)/µmH kT(r) The Attempt at a Solution [/B] I don't know where to...

Hello, I'd like to work in the above named center at the University of Georgia in Athens, Georgia under Dr. Henry Schafer. However, he's a professor in the chemistry department. I'm guessing if I go in the university as a physics graduate student I can't have him as a Ph.D advisor. However, is...

The "big bang" suggests that everything came from a single point. If this is true that how can there be no center? And if everywhere is the center, then the universe by definition has to be infinite. And if the universe in infinite, then how did it become that way?

If I fire an electron and positron bunch both in the same direction away from my experimental accelerator rest frame such that the electron bunch is fired with higher energy towards a "read end" collision with an already fired positron bunch and they collide a short distance away from the...

Homework Statement [G,G] is the commutator group. Let ##H\triangleleft G## such that ##H\cap [G,G]## = {e}. Show that ##H \subseteq Z(G)##. Homework EquationsThe Attempt at a Solution In the previous problem I showed that ##G## is abelian iif ##[G,G] = {e}##. I also showed that...

Homework Statement A 15-cm-diameter CD has a mass of 21 g . What is the CD's moment of inertia for rotation about a perpendicular axis through its center?Homework Equations I = (1/2)MR^2 3. The Attempt at a Solution I = (1/2)(0.21g).((15/2)^2) = 5.9*10^-4 kg*m^2 cant see what I am...

I'm having hard time finding the center of inversion of cubic diamond structure. At first I thought (2,2,2) would be the center of inversion, but (1,1,3), (3,3,3), (1,3,1), (3,1,1) (i.e. four atoms inside the cube) are not centrosymmetric about (2,2,2).

Homework Statement A 100 g ball and a 250 g ball are connected by a 34-cm-long, massless, rigid rod. The balls rotate about their center of mass at 150 rpm . Homework EquationsThe Attempt at a Solution I solved by first getting the center of mass, then converting rpm into m/s I treated rigid...

Homework Statement The rigidly connected unit consists of a 2.5-kg circular disk, a 2.8-kg round shaft, and a 4.2-kg square plate. Determine the z-coordinate of the mass center of the unit.Homework Equations ∑zm/∑m The Attempt at a Solution Circular disk: mass = 2.5 kg z = 0 zm = 0 Round...

Homework Statement The vector position of a 4.00 g particle moving in the xy plane varies in time according to 1 = (3i+3j)t +2jt^2 where t is in seconds and is in centimeters. At the same time, the vector position of a 5.95 g particle varies as 2 = 3î − 2ît^2 − 6ĵt. Determine the acceleration...

Homework Statement Let ##G## be a finite group and ##m## a positive integer which is relatively prime to ##|G|##. If ##b\in G## and ##a^mb=ba^m## for all ##a\in G##, show that ##b## is in the center of ##G##. Homework EquationsThe Attempt at a Solution Let ##|G| = n## and ##b\in G##. Note that...

Homework Statement A rigid cylinder of radius ##R## and mass ##\mu## has a moment of inertia ##I## around an axis going through the center of mass and parallel to the central axis of the cylinder. The cylinder is homogeneous along its central axis, but not in the radial and angular directions...

Homework Statement In the ammonia (NH3) molecule of the figure, the three hydrogen (H) atoms form an equilateral triangle, with the center of the triangle at distance d = 9.40 ✕ 10^−11 m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms...

Homework Statement "Find the center and radius of the circle that passes through A(1,1) and is tangent to the line y=2x-3 at the point B(3,3). (Picture of the graph: https://imgur.com/a/0wAnqcU) Homework Equations Here's a link: https://imgur.com/a/y71Z9GY The Attempt at a Solution Soo, I've...

Homework Statement A cylinder of radius a and mass m contains a point mass, also of mass m, located a distance ##a/2## from the symmetry axis. The cylinder is placed on an incline, which is initially horizontal, but is very slowly raised. Assuming the cylinder cannot slide on the incline, at...

Homework Statement A cylindrical conductor of length L and radius R, L » R, carries a charge Q. 1. Neglecting boundary effects; evaluate the potential difference between a point at distance r from the center of the cylinder, and the center. Assume r to be of the same order of magnitude as R but...

Homework Statement Two forces F1 →= 2i ^ + 3j^N acting on a mass m1 =1.5 kg, andF2→= i^+ j^N acting on a mass m2= 1.0 kg.The magnitude of the acceleration of the center of mass of the system is?

Homework Statement For ##S_3## compute the centralizers of each element and find the center. Homework EquationsThe Attempt at a Solution I found that ##Z (S_3) = \{ 1 \}##, ##C_{S_3} (1) = S_3##, ##C_{S_3} ((13)) = \{1, (13) \}##, ##C_{S_3} ((12)) = \{1, (12) \}##, ##C_{S_3} ((23)) = \{1, (23)...

Hello, I am trying to find out how to determine the center of gravity of a CubeSat present in an uniform sphere of radius R, using the initial data given by gyroscopes. The satelitte is equipped with magnetometers, gyroscopes, and accelerometers. By taking into account that the only values I...

The question is: The orange and blue cat are currently balanced on the see saw. The orange cat then eats a bird, which of the following could make the see saw balanced again? - I attached the picture that the question is referencing. And the possible answers are: A. Orange cat stays at same...

Homework Statement Find the centre of mass of a uniform hemispherical shell of inner radius a and outer radius b. Homework Equations ##r_{CoM} = \sum \frac{m\vec{r}}{m}## The Attempt at a Solution Using ##x(r,\theta,\phi)## for coordinates...

Homework Statement A wire carrying current I=7A is shaped as half circle of radius R=0.2m.The magnetic field B(in μT) at the center is : A)11.0(k) B)7.9(k) C)9.4(k) D)6.3(k) E)4.0(-k) Homework Equations B=(μ0 I)/(2πR) The Attempt at a Solution B = (4π*10-7 *7)/(0.2*2*π) * 0.5 (Multiply by 1/2...

Homework Statement determine the center of mass of a thin plate of density 12 and whose shape is the triangle of vertices (1,0), (0,0), (1,1). Then, using the appropriate pappus theorem, calculate the volume of the solid obtained by rotating this region around the line x = -2. Homework...

South Carolina is ready for the arrival of extraterrestrial visitors. On my way to Charleston yesterday, I visited the UFO Welcome Center in Bowman: Nobody was around. Maybe the caretaker was out for lunch? I didn't try to go inside because I might have fallen into a black hole or...

Homework Statement [/B] A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end. Starting from rest the heavier object moves downward and the lighter object moves...

Homework Statement a) [Solved] What is the threshold energy in the center of mass for production of an antiproton in a proton-proton collision? Make sure quantum numbers are conserved. (This one was easy and I manage to solve it) b) In a fixed target experiment calculate the proton beam energy...

Why is the density of matter greater near the galactic center?

Homework Statement Determine the B-field inside the middle of a circular loop of current. Homework Equations Attempt at using Ampere's law: ##\oint \vec{B} \cdot d \vec{l} = \mu_0 i## The Attempt at a Solution ##\oint B \cdot R d \theta = \mu_0 i \Rightarrow BR(2 \pi) = \mu_0 i \Rightarrow B...

Homework Statement The picture illustrates a simple pendulum and and two physical pendulums ,all having the same length ,L. Class their period in ascending order. Homework Equations T = 2π / ( I/mgh) I = Icm + mh2 Icm=(ML2/12) The Attempt at a Solution I have found the period for first...

Homework Statement A 25kg child is spinning on a merry-go-round of mass 150kg and radius 2m at a constant angular velocity of 1rev/s. The child slowly walks to the center of the merry-go-round. Treat the child as a point mass and the merry-go-round as a uniform solid disk, and neglect friction...

I want to do a cost estimation for an edge data center in Bakersfield, California. I don't know how big should the center be and i do not know how i can view the data traffic. Can anyone help?

Homework Statement each wire carrying 10 Amps a = 0.3 meter point o located in the center Homework Equations B = permeability constant * I / ( 2 ##\pi## r) r = distance between O and the wire r perpendicular to B and I A = carrying current into the page B and C = out of the pages The...

If the universe is very large relative to the observable universe and it is spherical, and the observable universe is well away from the outside region of the sphere, more towards the center, is spacetime approaching flat for the observable universe? I always assumed the answer is yes, but then...

I worked problem 2.28 of Nayfeh and Brussel's Electricity and Magnetism. The problem asks for the potential near the center of a charged hollow sphere, based on the near-field expansion given by equation 2.62, which is: ##\Phi=\frac{1}{4\pi\epsilon_0}[\frac{dq}{r^\prime}+ \vec r \cdot \int...

Masses $m, 2m$ and $\sqrt{3}m$ are located at points $P_1, P_2$ and $P_3$ on a circle $C$ so that their center of mass coincides with the center of $C$. Find the angles of the triangle $P_1P_2P_3$.

The Klingon Empire has opened a travel center in Stockholm, in its quest for world tourist domination. I wonder how many PF'ers work there.

Homework Statement We have a circle of radius 4 with center at the origin of a referential, and a circle hole in it of radius 1 and center at (-2,0). We're supposed to calculate the center of mass. 2.MY QUESTION. I know, by the usual formulas for calculating center of mass I get 2/15 as the x...

https://phys.org/news/2018-02-high-resolution-image-core-milky-reveals.html This is my first thread here so if I have done something wrong or placed it in the wrong place, I apologies in advance. Otherwise enjoy! I found the images amazing to say the least.

Homework Statement A spherical shell with radius R and surface charge density σ is sandwiched between two infinite sheets with surface charge den- sities −σ and σ , as shown in Fig. 2.46. If the potential far to the right at x = +∞ is taken to be zero, what is the potential at the center of...

I'm trying to model a sphere having force applied at position P in the following diagram: I know that this applied force will have an x and y component; the y component will propel it upwards, but what I am confused about is the x component of the force. I know that the x component will propel...

$\textsf{Find the center of mass of a thin plate of density}$ $\textsf{ $\delta=3$ bounded by the lines $x=0, y=x$, and the parabola $y=2-x^2$ in the $Q1$}$ $\begin{array}{llcr}\displaystyle &\textit{Mass}\\ &&\displaystyle M=\iint\limits_{R}\delta \, dA\\ &\textit{First Moments}\\...

Homework Statement Three 18-cm long rods form an equilateral triangle. Two of the rods are charged to +10 nC, and the third to - 10 nC. What is the electric field strength at the center of the triangle? Homework Equations $$ \vec{E} = \frac{k*q}{r^2} $$ The Attempt at a Solution 1. Draw...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] I did not understand what is meant by the center of the pattern here. a) I have ## \delta \theta_{hw} = \frac { \lambda }{Nd \cos{\theta }} ## For central maximum ## \theta = 0##, so central line has less width than...

I have been doing a study for a couple of years now on the off center fed dipole. I was very much in the dark on what to expect in the relationship between the off center fed (ocf) and a regular dipole. I asked many questions and most of the time I jumped to the wrong conclusions. I decided...

If we have a system of masses in motion, will the velocity of the center of mass always be given by the net momentum divided by (1/c^2 times) the total energy of the system?

Homework Statement Homework EquationsThe Attempt at a Solution I am having trouble understanding the setup as well as how to approach this problem . I am not understanding the orientation of the two pieces of the wire . They make angle 60° with each other , but then what does it mean when...

I have an odd question after making a rubber band car. I'm wondering if placement of my pairs of wheels has any affect on how fast or how far my car goes. It seems to be a very impractical design, but I do want to know the science behind it. My question is if I move two wheels all the way to...

Hi, In electrostatics, we have Coulomb's law for the electric field of a point charge. We can generalize to the electric field of a continuous charge distribution, using $$E=k\int r^{-2}dq.$$ It would seem, using the same argument that gets us to the previous equation, we could define the...