Centre of mass Definition and 219 Threads

Homework Statement Now, I know the centre of gravity can change depending on how close to uniform the gravitational field is, and it is where the weight appears to act from. But, what is the centre of mass? Ok, it is a constant; doesn't change; and in an uniform gravitational field the two...

Homework Statement a thin uniform wire is bent to form two equal sides AB and AC of triangle ABC , where AB=AC=5cm . the third side BC , of length 6cm is made from uniform wire of twice the density of the first . the distance of centre of mass from A is ? Homework Equations x centre of mass...

Homework Statement An unstable ion of mass ##M##, energy ##E## emits a massless particle of energy ##E_\nu## at angle ##\theta##. In the rest frame of the ion, find ##E_\nu^*## and ##cos \theta^*##. Ions are now accelerated to ##\gamma=100## and a detector with radius ##r=20m## is placed...

I have to calculate the centre of mass of the drawn hemisphere. I don't understand where I make mistakes. The process I followed on the above image is the following: (I) Here I simply translated position vector components from cartesian to polar coordinates. (II) Formula of x-component of...

Homework Statement A man of mass M stands on a railroad car which is rounding an unbanked turn of radius R at speed v. His center of mass is height L above the car, and his feet are distance d apart. The man is facing the direction of motion . How much weight is on each of his feet? Homework...

But in this lecture First example of car and truck no mass is given but he has solved for velocity of centre of mass. How?Is there any other alternative way to solve for velocity of centre of mass.

I know how to go from ground frame to centre of mass frame by subtracting velocity of centre of mass from the bodies.But I am not sure about how to go from centre of mass to ground frame.I think we should add velocity of centre o f mass.Right?

My teacher taught us how to locate position of centre of mass in semicircular disc She said circular disc is made up of two semicircles .It's centre of mass is located in centre .But When one of the semicircles is taken out from the circle , only one semicircle is left out.To locate the...

Homework Statement Find the centre of mass of solid cone. Homework Equations $$y_{cm}=\frac{1}{M}\int_0^Hydm$$ The Attempt at a Solution First I took thin disks. I got the answer when I assumed its thickness to be dy but then dysecθ would be more accurate if half angle of cone is θ since...

Homework Statement A solid metal rod with dimensions 5 x 2 x 1 is placed with one corner at the origin, such that 0≤x≤5, 0≤y≤2 and 0≤z≤1. The rods density is described by ρ(x) = (3x2 +10x) / 25 a) find the total mass of the rod b) find the x-coordinate of the centre of mass of the rod. Homework...

Hello, I uploaded an image of the question so it becomes clear my main doubt is which procedure should I follow 1) total object weight*PERP. Distance to toppling point=Moment of cylinder+moment of cone 2) moment of cylinder ≥ moment of cone I tried doing method two since they asked for least...

Hello, It's my first question here. So I'll try to give as much as information as I know Actually I am stuck with a problem of centre of mass derivation of a triangle with its base on the X axis and symmetric about it. The base is b and height is H As far as I know I have to imagine it as a...

Lets say we are sitting on a horse at the edge of a merry-go-round. You move faster relative to a point near the centre of the merry go round. Now most of the mass of this merry go round is at the edge i.e at the horse. So the moment of inertia at the horse is less. Correct me if I am wrong.

Hi I am doing an assignment where I roll a tin can filled with car oil. This will affect its rolling because it distorts its centre of mass, resulting in an awkward rolling motion. I have already done the experiment, the first revolution is the slowest one by a lot because it slows down a lot...

Homework Statement Lower surface of a plank is rough and is initially at rest on a horizontal floor. It's upper surface is smooth and has a smooth hemisphere place over it through a light string as shown. Find the trajectory of centre of mass of the sphere after the string is burnt. Homework...

Homework Statement a) Two astronauts, A of total mass 90kg and B of total mass 110kg are tied together by a light rope 15m long during a space walk. A starts to reel in the rope at her end. After 8.5s she has reduced the length of the rope by 5.5m. What distance does the centre of mass move in...

My original question was answered, but I would just like some clarification regarding one concept. In the derivation for the centre of percussion in this link (http://en.wikipedia.org/wiki/Center_of_percussion), what exactly is the variable A? How can it be determined (theoretically and/or...

"if kinetic energy of system of particles is zero, then linear momentum of that system of particles is zero but the reverse is not true. That is if linear momentum of a system of particles is zero, then the kinetic energy may not be zero" This is what I got from my text. Can you provide me with...

We define the position of the centre of mass of a system of ##n## masses as: $$\vec{r_{cm}} = \frac{\sum_{i=1}^n m_i \vec{r_i}}{\sum_{i=1}^n m_i}$$ Why is there no such thing as "centre of charge", defined for ##n## point charges: $$\vec{r_{cq}} = \frac{\sum_{i=1}^n q_i...

Homework Statement From my book-- "In motion of a planet round the sun we have assumed the mass of the sun to be too large in comparison to the mass of the planet. Under such a situation, the sun remains stationary and the planet revolves round the sun. If, however, masses of sun and planet are...

Homework Statement Two spheres, each of mass m and radius r are tied with a spring of spring constant k. The spring is stretched by a certain amount and the system is kept on a rough surface where friction is sufficient to prevent sliding. If one sphere is solid and the other is hollow, then...

Homework Statement The accompanying graph of position x versus time t represents the motion of a particle. If p and q are both positive constants, the expression that best describes the acceleration  of the particle is Homework Equations (A) a = – - p -– qt (B) a = –p + qt (C) a = p + qt (D)...

Given two masses falling towards each other under gravitational attraction, do they meet at their joint center of mass, assuming other gravitational forces are negligible?

Find the velocity of the centre of mass of a glass marble which rolls from rest down a gentle ramp inclined at an angle of 10o to the horizontal, without slipping, after it has travelled for a distance of 2.3 m. Moment of inertia of sphere: 2/5MR^2 Past paper question that I'm...

hey I got a questions and appreciate obv any reply. I am regarding to Capitel 12, page 128ff. from Gustafson, Sigal; Mathematical Concepts for Quantum Mechanics. So, let's consider on $L^2(\mathbb R^n)$ \begin{align} H_n= \sum_{j=1}^n \frac{1}{2 m_j} p_j^2 +V(x) \end{align} where...

Homework Statement A uniform plank of length l = 6m and mass M= 90kg rests on sawhorses separated by D = 1.5m and equidistant from the center of the plank. Cousin Throckmorton wants to stand on the right-hand end of the plank. If the plank is to remain at rest, how massive can...

I'm slightly confused as to how we discuss centre of mass frames in nuclear reactions. We have the reaction a(A,B)b. Before the reaction we can transfer to the centre of mass frame v_c = \frac{\sum m_i v_i}{\sum m_i} and note that the total energy before the reaction is E_{CM} =...

Homework Statement A machine part consists of a thin, uniform 4.00 kg (A) bar that is 1.50 m (X) long, hinged perpendicular to a similar bar, placed vertically downward, of mass 3.00 kg (B) and length 1.80 m (Y). The longer bar has a small but dense 2.00 kg (C) ball at one end (the ball...

A lamina comprises a uniform rectangular card ABCD where AB = 10 cm and BC = 12 cm with a circle of radius 3 cm cut out. The centre of the circle is 7 cm from AB and 4 cm from AD. How would I find the centre of mass for this lamina? I know to find the centre of mass for a uniform lamina we...

1. Find the centre of mass of a semi circular plate of radius R, the density of which linearly varies with distance, 'd' at the centre to a value '2d' at the circumference. 2. Xcom = (∫xdm)/M 3. I tried attempting the solution but I am not really knowing how to get dm in terms of dx

Homework Statement Two objects of mass m=3kg and M=7kg are held at a distance of 10 meter in space and then released. They move towards each other due to mutual gravitation attraction. Determine the location of their meeting of the object mass m Homework Equations r= mr1+ Mr2/m+M...

21. A 2.0-kg block is attached to one end of a spring with a spring constant of 100N/m and a 4.0-kg block is attached to the other end. The blocks are placed on a horizontal frictionless surface and set into motion. At one instant the 2.0-kg block is observed to be traveling to the right with a...

Could someone confirm if my method here is correct and if not maybe a few tips :) I have an L shape constructed of three "boxes" of side length a what is the centre of mass?I know that CoM= the sum of moments (m*a)/ the sum of masses So if I split the L into two parts, one box and two boxes...

If you have the function, (1+x3)1/2, find the indefinite integral. I have been trying different methods like substitution and rewriting it, but keep getting the wrong answer. I keep trying to find it using online integral calculators...

A thin stick of length L is balanced vertically on frictionless ice. What happens to the motion of the centre of mass if it gets a big push above the centre of mass of the stick? Does the centre of mass move? If so how do you work it out? This is more of an extra question I thought of when...

Ok so when I try to get the centroid of a semicircle using ∫rdm/∫dm, ∫dm = ρ∫dxdy for x^2, but now that the area is (0.5)∏(x^2 + y^2) what would ∫dm be? If I did use ρ∫dxdy I have to do some weird integration of sqrt(30^2 - x^2) which we haven't learned yet. If I do have to ρ∫dxdy how would I go...

Hi, experts I got a very naive question. I read the following sentence in a paper: "New results on the production of charged pions in p+p interactions are presented. The data come from a sample of 4.8 million inelastic events obtained with the NA49 detector at the CERN SPS at 158 GeV/c beam...

There are two problems I am facing, and in each one, they are introducing new terms in the integration but I don't understand how. Problem #1 Where I become lost is r=R(1-z/h) Why is this not just r=R(z/h)? Where does the 1-z come from? In this question, there is an...

Hi friends, I have an issue in solving a Acceleration of center of mass problem. Please Help me in solving this. Thank you all in advance. The problem is as: https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-prn2/q71/s720x720/1395961_1432382973655475_777941089_n.jpg Attempt...

Hi friends, I have Kinetic energy problem during collision. Please Help me in solving this. Thank you all in advance. The problem is as: https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-frc1/q71/s720x720/1380301_1432382870322152_49372184_n.jpg Attempt...

Calculate the centre of mass of the object shown below, assuming uniform density Object: http://i.imgur.com/zuOUyL7.gif Assume the origin, O, at the lower left, and the positive x-axis pointing to the right. 1) What is the x coordinate of the centre of mass, in terms of a? 2) If...

reference to Feyman lectures vol.1 topic 19.2 locating centre of mass Feyman gives us the law of pappus to find the centre of mass ,which he proves for semicircular disc and ring. But when i am trying to extend it to finding the centre of mass of a solid semi-circular solid hemisphere ,i...

I want to know whether I can use a point where all charge of a body can be assumed to be concentrated. Obviously such a point exists. I want to know whether it'll be the same point as centre of mass [as both are scalars and their integration SHOULD yield the same result] For example, if a...

An industrial tool is made from alaminar material occupyingthe region between thestraight lines y =2, y=1 2x and y =3−x. The density of thematerial varies and is given by thefunction σ(1 + x), where x is the horizontal distancefrom the y-axis and σ is aconstant. The mass of the...

Two blocks m1 and m2 are connected by an ideal spring of force constant k. The blocks are placed on smooth horizontal surface. A horizontal force F acts on the block m1. Initially spring is relaxed, both the blocks are at rest. What is maximum elongation of spring? i think it would be when...

So let's say I'm computing the torque as a result of the interaction between two electric dipoles in the lab frame. Let's imagine they are in some electric field. I then do : τ = r×F If I now switch to the centre of mass frame I have to find their position vectors from the COM. Why do...

Suppose the density of any point on a semicircular lamina {(x, y) : x >= 0, x^2 + y^2 <= r^2 is proportional to its distance from the origin. Compute the centre of mass. I am trying to figure out what is the density function for this case.

My book says (Foundations of Astrophysics): " The radial velocity ... can be found from the Doppler shift of the star's absorption lines: \nu_{r}=\frac{\Delta\lambda}{\lambda}c If the star you are observing is part of a spectroscopic binary system, you can separate the radial velocity of...

Homework Statement A block of mass "m" is placed on a triangular block of mass "M" , which in turn is placed on a horizontal surface as shown in figure. Assuming frictionless surfaces , find the velocity of the triangular block when the smaller block reaches the bottom end. Figure ...

Hey folks, I was doing some moments problems the other day, and I started considering centre of mass and centre of gravity and have gotten myself rather unsure. My textbook defines centre of mass as "the point through which a single force has no turning effect", which I have an intuitive grasp...