In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion.
In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.
The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system.
I hope this is self-evident to someone, I'm struggling.
I have a program that draws circles (n-gons really) of various sizes, but by translating-rotating-translating-rotating-..., not by x=sin/y=cos. That works as intended, but my wish is to offset the circle so that its center is (0,0) in...
Does the milkyway orbits anything ?? like sun orbiting center black hole of our galaxy
Does the milkyway orbits anything ?? like sun orbiting center black hole of our galaxy
i have this question bcoz
our moon moves towards(orbiting) Earth but can't reach or hit Earth bcoz Earth moves...
Hi,
This is a question about shear center location. I know exactly how to calculate the exactly location. But I have trouble quessing the first "Imaginary" location.
I have this picture
http://i46.tinypic.com/16jesgo.jpg
http://i49.tinypic.com/2v30xlk.jpg
Now you see that the shear center...
Homework Statement
A variable circle cuts x and y axes so that intercepts are of given length k1 and k2. Find the locus of center of circle
Homework Equations
The Attempt at a Solution
There must be four intercepts but only two are given.
A car of mass m moving East at speed v (v << c no need to use relativity) collides with another car of mass 2 m moving North with speed 3v.
a) What are the x and y components of the center of mass velocity of the system just before the collision?
b) If the cars stick together during the...
HELLO
Can someone help me locate the center of gravity for my vehicle design? all the parts, dimensions and mass of the parts of the design are known. Is it possible to locate for the COG of it? Thanks!
Homework Statement
13 equal charges are placed at the corners of a regular 13 sided polygon. What is the force on a test charge at the center?
Homework Equations
Coulomb's law
Principle of Superposition
The Attempt at a Solution
Coulomb's law gives an answer of 0, but it is...
Homework Statement
Three positive charges, A, B and C, of 3 × 10-6, 2 × 10-6, and 3 × 10-6 Coulombs respectively, are located at the corners of an equilateral triangle of side 0.2 meters.
Find the magnitude in Newtons/Coulomb of the electric field at the center of the triangle...
Homework Statement
a 90 kg block 1 and 360 kg block 2 are on opposite ends of a 300 kg slab of length 12.0 m which is on a frozen lake. assume no friction between slab and ice. block 2 moves 4.0 m towards block 1 while block 1 moves 2.50 m towards block 2. how far does the slab move?
Homework...
Hi Guys, I just want to know the effect of varying center of mass in a vehicle, specifically in a line following robot, I am going to put load on it, thus center of mass will vary, then i will study how will the varying center of mass affect the response of the line following robot, can anyone...
Homework Statement
Find the Y component of the Center of Mass
http://img607.imageshack.us/img607/7122/83370796.png
Homework Equations
∫(r*dm)/M
The Attempt at a Solution
I keep coming up with (2/3)B but i know since that there is more mass near the origin axis, it should be...
Potential at the center of an electric dipole is zero. This doesn't make intuitive sense, how can work required to bring an arbitrary charge from infinity to the center of a dipole be zero? Imagine a charge at some distance on horizontal bisector of the dipole, it will deflect from the...
Homework Statement
Find volume of a sphere with radius R with a hole drilled through the center of radius b. (b<R)
Homework Equations
cos thera = adj / hyp
The Attempt at a Solution
4\,\int _{0}^{\arccos \left( {\frac {b}{R}} \right) }\!\int _{0}^{\pi
}\!\int...
Homework Statement As a result of a temperature rise of 22 C, a bar with a crack at its center buckles upward. If the fixed distance is L = 2.79m and the coefficient of linear expansion is α = 2.79×10-4K^-1, find the distance x to which the center rises.
Homework Equations i used...
I'd like to know why a ray of light passing through the optical center of a convex lens does not get refracted at all. According to my knowledge, a ray of light will not get refracted if the angle of incidence is zero i.e. it is along the normal. With this in mind, I see how a ray traveling...
Center of Mass Derivation..Doubt :(
Homework Statement
Guys,I don't seem to understand how the general equation for Center of mass was derived.I mean,yeah,i get that in a rod,or other symmetric structures,it should lie at the point of symmetry more or less,How waz the general equation...
Homework Statement
Here is the question along with the solution:
I was wondering why the ICZV is at point A. Is it because the string is not slipping and thus the yo-yo is essentially "rolling" on the surface of the rope? Kind of like a bike wheel rolling on the ground?
Homework Statement
Hey
In my assignment I am writing about beamdeflection, but there's some things i really can find out how to do.
I need to explain area moment, moment of inertia and the center of gravity, i need to explain this with the help of integration.
Under her I've inertet...
Ok we know for a Dipole the direction of Electric Field for points on the the dipole axis is in the direction of Dipole Moment(from -ve to +ve charge) rite? Now we also know that fields emanate from +ve charge and extend towards -ve charge. So what will be the direction of Electric Field at the...
there is a similar case here :https://www.physicsforums.com/showthread.php?t=296966
so I've tried it and what i did was to equate both individual moment of inertia about z axis (and later applied parallel axis theorm) with negative mass for hole. added both these and found out Ix = M/4...
Homework Statement
In the image below, calculate the center of mass (x-bar,y-bar) of the composite body.
Homework Equations
I've used all of the equations for area for the shapes needed (triangle, square, circle).
The Attempt at a Solution
I have attached my calculations and...
Homework Statement
Energy, Center of Mass: As a project your team is given the task of designing a space station consisting of four different habitats. Each habitat is an enclosed sphere containing all necessary life support and laboratory facilities. The masses of these habitats are 10 x 105...
Homework Statement
So the problem starts out like this
Stick of the Gods! You hold one end of a stick, but it has no other end. It simply extends into infinity. Its one-dimensional density distribution is given by:
λ=(λinitial)times(e^(-x/L))
λ is the density
The problem doesn't state what...
Homework Statement
I need to find the center of mass of the given figure attached. I am given the density (7850 kg/m^3) and a thickness of 0.3 cm (not sure where this goes)
Homework Equations
Just some things I need to verify:
When finding the x-bar of the function y=x3 using the equation...
Just some things I need to verify:
When finding the x-bar of the function y=x3 using the equation:
\bar{x} = \frac{∫\tilde{x}dm}{∫dm},
Is my \tilde{x} going to be the x distance(which will just be "x") times x3?
Also, will x3 be in the denominator just before "dm"?
The same process...
Homework Statement
An appliance box has a square base with sides of length L, and has rectangular sides with a height of 3L. The top of the box is missing. The box is made from cardboard of uniform thickness and density. What is the height of the center of mass of this open box, with respect...
Hello,
I am struggling with what was supposed to be the simplest calc problem in spherical coordinates. I am trying to fid the center of mass of a solid hemisphere with a constant density, and I get a weird result.
First, I compute the mass, then apply the center of mass formula. I divide...
can we find the center of the universe by measuring the deviation from theoretical value of the shape of comet's orbit when compared to real shape of comet's orbit.
Homework Statement
The total length of the composite body is 4.5 feet. Before the propellant is burned, the projectile weighs 23 lbf. After the propellant burns, the remaining projectile weighs 16 lbf. Before the propellant is burned, the mass center is located 2.6 feet from the projectile...
Homework Statement
I need to find the center of gravity of a horizontal cylinder that has water in it, the level of water changes so I need to determine a relation between the diameter occupied by the water and the masses, those are my guesses.
I solved the problem where i have the standing...
Homework Statement
A proton is moving along the main axis of a uniformly charged thin ring. The charge density on the ring is 5.0 nC / cm and the ring radius is 1.0 cm. Initially the proton is 2.0 cm (along the axis ) from the center of the ring with the velocity towards the center of the...
Homework Statement
Equate the expression for centripetal acceleration with the gravitational acceleration to show that the central parts of the galactic rotation curve are consistent with rigid body rotation.
The attempt at a solution
Say a star near the galactic center has mass m and the...
Hi,
I am trying to find out the roll center of a truck's cab. I went over a similar thread in which jack action explained the concept of roll center. But I am having trouble applying it to something like the cab.
It does not really have wheels or a multi-link suspension system like a car...
Homework Statement
See the attachment below. The solution is stated to be number 4 (option a). I am having trouble understanding this. It seems that a majority of the sculpture's mass (in terms of its y-component) is well below the vertical component of point 4, and hence should lower the CM...
Homework Statement
A man with mass m1 = 69.0 kg stands at the left end of a uniform boat with mass m2 = 163.0 kg and a length L = 2.8 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...
Hi,
I am having some difficulty doing the integral
∫d^{3}v1d^{3}v2 | \overline{v1}-\overline{v2}|, where u1\leq|v1|,|v2|\lequ2, and \overline{v1} means vectors.
It seems better to evaluate it in the center of mass frame, by substitution \overline{v1}+\overline{v2}=\overline{V}, and...
Homework Statement
A person with mass m1 = 67.0 kg stands at the left end of a uniform beam with mass m2 = 91.0 kg and a length L = 3.3 m. Another person with mass m3 = 56.0 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 12.0 kg (assume that the medicine...
Homework Statement
To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 92.0cm long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a...
What are (a) the x coordinate and (b) the y coordinate of the center of mass for the uniform plate? Since the plate is uniform, we can split it up into three rectangular pieces, with the mass of each piece being proportional to its area and its center of mass being at its geometric center. We’ll...
Homework Statement
A solid metal cylinder of radius R and length L, carrying a charge Q, is surrounded by a thick coaxial metal shell of inner radius a and outer radius b. The shell carries no net charge. Find the potential at the center, using r=b as the reference point.
Homework...
Homework Statement
A chimney (length L = 82.6 m, mass M = 2280 kg) cracks at the base, and topples. Assume:
- the chimney behaves like a thin rod, and it does not break apart as it falls
- only gravity (no friction) acts on the chimney as if falls
- the bottom of the chimney tilts but...
Homework Statement
A ground spherical conductor of radius a lies at the center of a uniform spherical sheet of charge QB and radius b.
a) How much charge is induce on the conductor's surface? Ans(-QBa/b)
Evaluate V(r) at position between the conductor and the sheet and outside the sheet...
Homework Statement
NH3 (ammonia) that is shown in the picture. These three hydrogen-atoms is formed as triangle.
Center of the triangle has a distance d = 0.940 from each hydrogen atom.
The nitrogen atom located in the vertex of a pyramid in which the three hydrogens defines "the base"...
Ive been given this table in a lecture (attached) and I'm not sure what they're using to fill in the columns of Xi an Yi, it looks like it should just be half of each section in Yi, but that is not the case in Xi, can anyone please explain this to me.
Thanks =)
Wiley Coyote and his Acme rocket, together having inertia of 1000 kg, are speeding after Roadrunner. Upon seeing a large brick wall in his path, Coyote tries to slow down. Unfortunately, he’s still going 5 m/s when he runs into the wall. The wall is not affected, but the rocket crumples (the...
Homework Statement
There is a section in my book that has the same title as the title of this discussion topic. I understand the math just fine, so this is a conceptual question. In the book the cross section is shaped and oriented like a C, and it shows the shear flow flowing...
I'm just learning how to use Ansys Workbench 13 to analyze static structures. I need to analyze the deformation of a simply supported beam with a concentrated force in the center vertically downward. I have a 3D model of this beam created in Solidworks.
How do I create a force in the center...
When looking at example 3 in this pdf: http://www.physics.isu.edu/~hackmart/centerofmass.pdf where it shows how to find the Center of Mass of a Nonuniform Rod. I was wondering when or what you have to know in order to integrate over dm rather than changing the variables in terms of dx.
I am using the textbook called Classical Mechanics by John R. Taylor.
Z = 1/M ∫ ρ z dV = ρ/M ∫ z dx dy dz
On page 89, example 3.2, it says:
"For any given z, the integral over x and y runs over a circle of radius r = Rz / h, giving a factor of πr2 = πR2z2 / h2."
I wish the book would...
A solid is formed by rotating the region bounded by the curve y=e^(-6x/2) and the x-axis between x=0 and x=1 , around the -axis. The volume of this solid is (pi/6)(1-e^(-6)). Assuming the solid has constant density, find the center masses of x and y.
center of mass (x or y)=...