Center of mass Definition and 900 Threads

I found this video on youtube which is trying to explain Fourier transform using the center of mass concept At 15:20 the expression of the x coordinate is given in the video. I believe it is wrong, and it should be: ##\frac{{\int g(t)e^{(-2 \pi ift)}.g(t).2 \pi f.dt}} { \int g(t).2 \pi...

Let’s say we have a boat whose longitudinal axis is the y-axis (which goes into the screen in the figure below) standing upright in a still water . ##S## is the Center of Mass of the boat and ##C## is the Center of Mass of the displaced water.On ##S## lies the force ##\mathbf W##...

I know that if they had the same density they would have the center of mass at 1,5 m. But now that they don't the center of mass will be shifted towards the part of the rod with higher density. they will have their center of mass where they have equal mass p1*v=p2*v now i don't know how to...

I was talking to someone about the equilibrium of fluids and we reached at some stage where we had to prove that in an external field the translational forces add to zero along with moments (torques) should also add to zero. The first one was quite easy but during the discussion of second...

<work done a system> a) w=5N*(0.4m)=2J I think this is right, but b) center of mass initial = ((0.5kg)(0.05m)+0.5kg(0.65m))/1kg = 0.35m center of mass final = ((0.5kg)(0.45m)+0.5kg(0.4+0.1+0.3+0.25))/1kg = 0.75m I'm not sure for this one... How can I calculate the displacement of the...

Figure 4 shows three point masses glued to the vertices of a massless triangle of side L=2.0 m. Two of the massess are m=0.75kg and the other mass is twice that value, as shown in the figure. The device is allowed to rotate about point A in a verticle plane about the centre of the larger mass...

I believe they are the same?I think i am wrong.

In classical mechanics, the energy of a system of particles (say with 2 particles) in an external field is given by $$E=\frac{1}{2}m_1|\vec{v}_1|^2+\frac{1}{2}m_2|\vec{v}_2|^2+V(\vec{r}_1)+V(\vec{r}_2)+V'(|\vec{r}_2-\vec{r}_1|)$$ Where V is the potential energy of the external field, and V' is...

Summary: I know that in order to keep inverted pendulum balanced when it leans forward, I should accelerate the bottom of it, but what is the force which is applied to center of mass of the pendulum with balances torque due to gravity? Is it inertial force? We assume that our inverted pendulum...

I tried to use the Lorentz transformation: ##E^{*}_{\gamma }=\gamma _{cm}E_{\gamma }-\beta _{cm}\gamma _{cm}p_{\gamma }## We have a photon, so it becomes: ##E^{*}_{\gamma }=\gamma _{cm}E_{\gamma }(\beta _{cm}-1)## Unfortunately, the solutions say that the correct way is to use the inverse...

I begin by drawing the problem. Let the center of the bigger sphere on the left by the origin for the system. Calculating ##x_C = \frac{10 \times 1.1 + 20 \times 2.15}{50+20+10} = \frac{54}{80} = 0.675\; \text{m} \;= \boxed{67.5 \; \text{cm}}\;##. Problem is, doesn't match the answer in the...

is this method even possible? anyways here is my attempt Step1) y= 2H/3 ( H is the height of the cone) step 2) we take the density (ρ)= 3M/π R2 H. The problem i am facing is to Find "dm"

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I have known and used this theorem for a long time solving problems ("Calculate the CM of the some given shape"). I took the theorem to be "obvious" and didn't know it could be proved (and that indeed it was a theorem at all). I can make no attempt at the proof. Any help would be welcome.

Not sure what I went wrong here, anyone can help me out on this? Thanks. EDIT: Reformatted my request. Diagram: So as far as I know to calculate the center of mass for x, I have to use the following equation: COM(x): ##\frac{1}{M}\int x dm## And I also figured that to find center of mass, I...

I tried getting the velocity of a which by using constraint came out to be 3 and by using the eqn for vcom i got the ans as 3.5 i just want to confirm is this the correct answer

The center of mass of someone's thigh, shank, and foot are located at the following coordinates: Thigh: (2.7, 3.2) Shank: (2.1, 2.5) Foot: (1.5, 1.9) If the masses of them are respectively 9.6, 2.9, and 0.9 kg, where is the location of the entire leg? ANSWER: CM = (2.5, 3)I'm having trouble...

The red dots show the CM of each block. ##x## is the amount by which the upper block overhangs the lower block. The blue (dashed) line shows the CM of the combination. For maximum overhanging, this line lies on the edge of the table below. By symmetry, the CM lies exactly midway between the two...

Suppose there is a photon with momtum p=h/lambda moving in the positive x-direction. Suppose it collides with an electron at rest and is completely absorbed by the electron, and that after the collision, the electron moves to the right with the same momentum of the photon. This seems...

Hello I have learned about conservation of momentum, Newton's law (1st, 2nd, 3rd law + free body diagram), conservation of energy and finding center of mass of several 2 D and 3 D shapes (non - calculus method). I watched youtube video about two objects connected by horizontal spring and in...

I don't understand what I am supposed to do. I know how to find the acceleration of the system, but I am not sure how to find the com acceleration. My guess would be something along the lines of xcom = (m1a1*x + m2a2*x)/(m1a1 +m2a2). Then do the same for the y axis. Then to find the velocity all...

What are the steps to calculating the center of mass for this object? I don't want a numerical answer just the theory. I understand I need to calculate COM for all axis, we know in the Y axis it's dead centre because of symmetry but I don't know how to do it for the others. A hint would be...

I was able to find the y and z axis. To find the x-axis I was assuming they would be the same for both of the slab parts and since the center of mass is the middle of the cube it should be halfway between 14.0 cm, which is 7.0cm. I can't think of any other reason why it would not be.

The object is: My attempt at a solution: I divided the object into 3 different rectangles and found the coordinates for the center of mass of each one, considering the origin at point "O". Then I found the mass of each rectangle, assuming the object has an area density of σ. m1 = 15σ; m2= 6σ...

It is known that the center of mass of an isolated system will assume the same location no matter what internal forces there are (as long as no net external force occurs). My first question is if there exist two bodies of masses m1 and m2 in some space that has no friction, gravity, or...

I've attached the problem and solution as picture. To my understanding, the gear E and the rod OB are taken together as the rotating rigid body. However, the equations of motion and (##∑F = macm##) are applied to the center of mass of the rod, G, rather than the center of mass of the rigid body...

Homework Statement Find the center of mass of a homogeneous solid cube with side ##L## analytically. Homework Equations None. The Attempt at a Solution I don't understand how to find the center of mass on three dimensions. I know that since it is homogeneous, if I center the cube on the...

Homework Statement Find the center of mass of the next plate if: A) Is homogeneous B) Its density per unit mass is ##\sigma=Axy##, where ##A## is a constant. Homework Equations ##X_{cm}=\frac{\int\sigma x dA}{\int\sigma dA}## ##Y_{cm}=\frac{\int\sigma y dA}{\int\sigma dA}## The Attempt at a...

Homework Statement Three spheres are placed around a coordinate grid: one of mass m at the bottom-left, one of mass 3m a distance of 3L above the first, and one of mass 2m a distance of 4L to the right of the first. 4 points between these three spheres are labeled: A near (1.3L, 1.5L), B...

The set-up of the system is like the following: The thing is, a weight was attached to the meter stick and it was placed in different locations. Then the system composed of the meter-stick and the added weight was then released and the time it took for the meter stick to hit the floor was...

Homework Statement A person of mass ##m## stands at the left end of a boat of mass ##M## and length ##L##. Both the person and the boat are initially at rest. The coefficient of kinetic friction between the boat and the water is ##\mu##. If the person starts moving to the right, what is the...

Homework Statement A cylinder with a mass of M and radius R is attached to a spring with a constant of k. The attachment always stays the same as described in the picture. The cylinder is moved to the right and the released, and it rolls without slipping (pure rolling). What will be the...

Homework Statement if the black dot is assumed by (0,0).find the center of mass coordinate of this triangle [/B] i'm sorry but since the pic won't show ill attach the link here https://ibb.co/4Ptw5T7 <Moderator's note: picture added> Homework Equations centroid is 2/3 of median [/B] using...

It’s essentially a question about cross product identities. I want to analyze a problem in a frame of reference which is rotating with angular velocity ##\vec \Omega## relative to an inertial frame. In this non-inertial frame, we have a rigid body rotating with constant angular velocity ##\vec...

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...

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 (Problems/diagrams referenced are attached as images.) Homework Equations Net torque about an origin = time derivative of the angular momentum vector about the same origin. The Attempt at a Solution I've solved these problems before, but I'm now looking back at them and...

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 In the figure below, a constant horizontal force app of magnitude 18 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 19 kg, its radius is 0.11 m, and the cylinder rolls smoothly on the horizontal surface. (a)...

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 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 A mass m_1, initially moving at a speed v_0, collides with and sticks to a spring attached to a second, initially stationary mass m_2. The two masses continue to move to the right on a frictionless surface as the length of the spring oscillates. At the instant that the...

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?

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 Four equal discs of mass ocuppy the vertices of a square frame made by four rigid bars of length and negligible mass. The frame is at rest on a horizontal table, and it can move with negligible friction. An instantaneous impulse is transmitted to one of the masses, in the...

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...