Center of mass Definition and 900 Threads

Two hollow spheres, both the mass and radius R M , which are rotating around a center of mass ( CM ) , with an initial period To, are kept distant from each other by an ideal wire with a distance of 8R. At a given instant a motor is driven by wrapping the wire and making the two spheres meet...

Homework Statement two particles of 2 kg and 3 kg are at rest . a 6 N force is exerted on the 3 kg particle at t=0. what is the speed of the center of mass at t=5s? Homework Equations F=ma v=u+atThe Attempt at a Solution first i applied f=ma to the 3 kg object and got 2 as the accn. And...

Hi New member here! 1. Homework Statement In the figure one-fourth part of a uniform disc of radius R is shown. The distance of the center of mass of this object from center ‘O’ is ………………………. Given: For a semi-circular disc with origin of co- ordinate system at the center of circle, the...

Hello. Suppose I have a coordinate system with the origin at the center of mass at rest of some rigid object and I wish to calculate the total change in angular momentum of the object with respect to it's center of mass. If I apply a torque to the object, that also happens to be an unbalanced...

Homework Statement The attached diagram shows a uniform density hollow cylindrical shell with a solid bottom and an open top. It has radius R and height h. Find the height for the center of mass of this cylinder, taking the origin of the coordinate system at the center of the bottom. Use "pi"...

Homework Statement A shell is shot with an initial velocity http://edugen.wileyplus.com/edugen/shared/assignment/test/session.quest2529559entrance1_N10030.mml?size=14&ver=1436312588112 of 17 m/s, at an angle of θ0 = 63° with the horizontal. At the top of the trajectory, the shell explodes into...

Homework Statement The figure shows a composite slab with dimensions d1 = 11.6 cm, d2 = 2.85 cm, and d3 = 13.4 cm. Half the slab consists of aluminum (density = 2.70 g/cm3) and half consists of iron (density = 7.85 g/cm3). What are (a) the x coordinate, (b) the y coordinate, and(c) the z...

Homework Statement [/B] 2 masses connected with a solid rod .distace between them is 2L , total mass is M . B total mass is m ,length L can freely move between A and A' on flat and frictionless surface. all collisions are elastic. at the beginning B was stuck to A and all the...

Let's say a kid is playing basketball. He has a running start, jumps and while he is the air he shoots. There are no external forces at the time he shoots (disregard the minimal airdrag). If there are no external forces, shouldn't the center of mass after he shoots be the same as it was before...

Homework Statement Find the center of mass of a hemisphere of radius R. Homework Equations R_cm = (rho/M) Integral[ (vector r) dv] dv = r^2 Sin[theta] dr d[theta] d[phi] The Attempt at a Solution [/B] In spherical polar coordinates, vector r = r r-hat, so the argument of the integral should...

Hi, I'm having a discussion with someone on the plausibility of the physics in a science fiction movie (I know, very efficient use of time!). There's a scene with a space station shaped like a ring. It has a center body that is attached radially to one edge of the ring. This space station is...

For a tapered beam of constant density the center of mass is calculated as the mean of the mass distribution along the central axis, the center of gravity is calculated by getting the equilibrium of the angular moments to the left and right of a fulcrum moving along the horizontal beam. The...

Homework Statement [/B] A shperical shell of mass = 1kg and radius 2.0cm is released from rest at the top of an inclined plane at a height of 1.00m. The ball rolls down the incline without slipping, what is the velocity of the center of mass at the bottom of the incline.Homework Equations I'm...

Homework Statement A railroad flatcar of mass Mc can roll without friciton along a straight horizontal track as shown in the diagram. Initially a man of mass Mm is standing on the car which is moving to the right relative to the ground with a speed of vi. What is the change in velocity of the...

Homework Statement A dog of mass M is standing on a raft so that he is a distance L from the shore. He walks a distance d on the boat toward the shore and then stops. The boats has a mass of Mb. Assume no fricton between the boat and the water. How far is the dog from shore when he stops...

Homework Statement A 55 kg man is standing on a 65 kg and 4.0 m length canoe that floats without friction on water. The man walks from a 0.75m from one end of the canoe to another point 0.75 from the other end of the canoe. What distance does the canoe move? Homework Equations Center of mass...

First of all, I am sorry if this is in the wrong subforum; I'm not sure if astrodynamics should be under astronomy. The post is also fairly long. My problem is that in my derivation of the center of mass of a binary system, I get a conflicting result for the distances of the center of mass to...

I have found via integration that the y coordinate is $$y =h/2 = 120 mm$$. The x coordinate is $$x = \frac{-4r}{3\pi} = -51.9mm$$ and the z coordinate is $$z = r - \frac{4r}{3\pi} = 69.1 mm$$. I have no answers in my textbook so can't confirm whether i am correct or not.

Homework Statement https://courses.edx.org/static/content-mit-mrev~2013_Summer/problems/MIT/rayyan/check_points/Pictures/BK85.png A horizontal uniform bar of mass 220 kg and length L = 3.0 m is placed on two supports, labeled A and B, located as shown in the diagram. A block of mass 30 kg is...

Homework Statement Where's the COM Homework Equations The COM of a right triangle is a third of an edge apart of the right angle vertex The Attempt at a Solution Edge AC: ##\frac{50}{\cos 20^0}=53.2## Two thirds of edge AB: ##\frac{53.2\cdot 30^0\cdot 2}{3}=30.7## One third of edge BC...

Homework Statement A frog sits on the end of a long board of length L=5m . The board rests on a frictionless horizontal table. The frog wants to jump to the opposite end of the board . What is the minimum take-off speed (in s.i. Units) i.e.,relative to ground 'v' that allows the frog to do the...

Homework Statement My question is this: When finding center of mass, can you do so using spherical/cylindrical coordinates, or must you put it in cartesian coordinates? If you can use spherical/cylindrical coordinates, how do you set up the triple integrals ? Thank you. Homework...

Homework Statement Consider a solid hemisphere of uniform density with radius R. Where is the center of mass? z=0 0zR2 z=R2 R2zr z=R Image is provided. Homework EquationsNoneThe Attempt at a Solution Answer A and E do not seem logical. I thought it was answer C from my eyes. Center of...

Homework Statement Homework Equations I don't know how is it related to center of mass. The Attempt at a Solution I don't know how to begin. Thanks a lot for your help !

Homework Statement A meter stick is 200 g. A mass of 1 kg is placed in 20 cm, and another mass of 5 kg is placed in 100 cm. So the diagram will be like: Homework Equations Why do we have to include M2? And why is the mass of M2 is 200g? Isn't the whole meter stick weight...

Homework Statement Where is the difference between center of support of equilibrium and center of mass of system. For example we are given a ruler with length L and mass M and two builds with mass m1 and m2 on its edges. Homework Equations http://imgur.com/PiGA817 The Attempt at a Solution I...

Homework Statement 3.) What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)...

In the above figure, a small weight is placed at 2 cm (0.02 m) from the center of the rectangular prism. Let's call the mass of this small weight (M1) and the mass of the entire body including the small weight (M) Given the dimensions above, I want to know how to calculate the height of center...

Hey everyone! I recently worked through finding the moment of inertia of a cylinder with a cylindrical cavity off center, and I wish to further deepen my understanding of calculating the center of mass of such objects. So I made up the following problem: Homework Statement Find the center of...

Homework Statement mass = M radius = r rot. inertia = i height = h Sphere of mass M is released from rest at the top of an inclined plane. The speed of the center of mass at the bottom of the incline, without friction, is sqrt(2gh). I need to find the velocity of the center of mass assuming...

Homework Statement I would like to calculate the position of the center of mass of the body on the figure. http://kepfeltoltes.hu/150302/161353224K_pkiv_g_s_www.kepfeltoltes.hu_.jpgHomework EquationsThe Attempt at a Solution I read a way of solution: Theorem of Pappus It states that if we...

Homework Statement A man with mass m1 = 55 kg stands at the left end of a uniform boat with mass m2 = 175 kg and a length L = 2.7 m. Let the origin of our coordinate system be the man’s original location as shown in the drawing. Assume there is no friction or drag between the boat and water...

Homework Statement I am trying to understand a substitution used to solve for the center of mass of a solid uniform hemisphere as in this post: https://www.physicsforums.com/threads/solid-hemisphere-center-of-mass-in-spherical-coordinates.650663/#post-4151797[1] I completely understand the...

Homework Statement [/B] I don't understand what I'm doing wrong with this problem: An old club-ax consists of a symmetrical 8.3 kg stone attached to the end of a uniform 2.9 kg stick. The stick is 98 cm long, and the 18 cm long stone is drilled through its center and mounted on one end of the...

Homework Statement Use Mach’s restatement of Newtonian mechanics to show that if we define the centre of mass of two particles according to, ⃗ r = (m1 ⃗ r1 + m2 ⃗ r2) / (m1 + m2) then the center of mass moves according to the equation, ⃗r = [(m1 ⃗u1 + m2 ⃗u2) / (m1 + m2)]t + ⃗r0 where ⃗r0 is...

Homework Statement A cart of mass m moving at 12 m/s to the right collides elastically with a cart of mass 4.0 kg that is originally at rest. After the collision, the cart of mass m moves to the left with a velocity of 6.0 m/s. Assuming an elastic collision in one dimension only, what is the...

Good night! Please, what happens to an object (eg a spaceship) placed exactly in the center of mass of a binary star system (composed by two similar stars)? Would it be compressed by a huge gravitational mass (something like the mass of both stars)? Would it be stretched and torn? Or would it...

Is center of mass a vector quantity. If so then how? Is it directed towards Earth's center?

what is the difference between center of mass and center of gravity ? please explain it in an easy way ...

Homework Statement It is a question I asked to myself because I need to reply to another one. I imagined this case: http://imageshack.com/a/img912/7730/R964Vq.png The step2 needs the energy E1, the step3 needs nothing because the gravity is 0 (I imagine the device between the Earth and the...

I am a beginner and this is my first post. We know torque ## \vec T = \vec r × \vec F ## Now, should r be fixed in magnitude? I mean can I calculate torque only if the particle is rotating at a fixed distance around a fixed axis? I am having this idea because torque is explained (from where I...

Homework Statement Two men with masses 70 kg and 120 kg rotate at 1 rpm on a frictionless surface and are attached by a 15 m rope. If they pull the rope so that only 10 m is between them when they rotate, how long does it take to make 1 revolution? Homework Equations Angular Momentum and...

Homework Statement Suppose that a system consists of several bodies, and that the position of the center of mass of each body is known. Prove that the center of mass of the system can be found by treating each body as a particle concentrated at its center of mass. Homework Equations ## \vec R...

Homework Statement A uniform horizontal beam of length 8.00 m and weight 200 N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53.0 degrees with the horizontal. If a 600-N man stands 2.00 m from the wall, find the tension in the cable and...

Homework Statement Find the center of mass of an equilateral triangle with side ##a## Homework Equations ## \vec R = \frac{1}{M} \int \vec r \ dm ## ## dm = \frac{M}{A} dx dy ## ## A = \frac{\sqrt{3}}{4}a^2 ## The Attempt at a Solution I set a pair of orthogonal axis ##(\vec x,\vec y)##...

If an object that has more mass at one end of it was dropped, how come the heavier end would be facing closer to the ground than the lighter end? For instance, a toliet plunger is dropped, and the heavier, rubber end of it positions itself at the bottom during the fall. What is this called?

Homework Statement Find the x-coordinate of the center of mass of the lamina that occupies the region cut from the first quadrant by the lines x = 6 and y = 1 if the density function is p(x,y) = x + y + 1 Homework Equations Mass = ∫∫spdσ X Coordinate of center of Mass = Myz/M Myz = ∫∫sxpdσ...

Hello all, this is my first post here. I will try to phrase it as best I can, my physics background is weak, so please be patient, and thanks in advance for your help! I tried researching simple pendulums but couldn't quite find an answer. Suppose a person is suspended, prone, from a pendulum...

1. Homework Statement The 4 black bars have constant linear density. In terms of L, find the coordinate of the center of massHomework Equations M0 X = summation of (MiXi) The Attempt at a Solution I understand most of the solution, except the answer key says one thing I don't get M/sqrt(2) at...

A uniform rod of length 2L and mass 2m is bent on its center at a right angle. The rod hangs down from the ceiling using a thread, so that one part, AB, is horizontal, and the other part, BC, is vertical. The question is what's the distance (x) between the suspension point D to the point A (the...