Center of mass Definition and 916 Threads

Homework Statement A solid sphere of density ##ρ## and radius ##R## is centered at the origin. It has a spherical cavity in it that is of radius ##R/4## and which is centered at ##(R/2, 0, 0)##, i.e. a small sphere of material has been removed from the large sphere. What is the the center of...

Homework Statement All three disks are made of sheet metal of the same material, and the diameters are 1.0 m , 2.0 m , and3.0 m . Assume that the x-axis has its origin at the left-most point of the left-most object and it points to the right. Part A) Determine the location of the center of mass...

Homework Statement All three disks are made of sheet metal of the same material, and the diameters are 1.0 m , 2.0 m , and3.0 m . Assume that the x-axis has its origin at the left-most point of the left-most object and it points to the right.Determine the location of the center of mass of the...

Homework Statement An 8.0-kg object is sliding across the ice at 2.34 m/s in the positive x direction. An internal explosion occurs, splitting the object into two equal chunks and adding 16 J of kinetic energy to system. The explosive separation takes place over a 0.16-s time interval. Assume...

Homework Statement Homework Equations triple integrals, center of mass The Attempt at a Solution I set up the triple integral x: lower limit 0 upper limit 1 y: lower limit 0 upper limit 2 z: lower limit 0 upper limit 1 ∫∫∫ δ(x,y,z) dx dy dz => applied the limits for x, y and z, and...

On page 252 of Kleppner's Introduction to Mechanics (2d. Ed.) in Example 7.5, Kleppner analyzes the forces and torques on a uniform rod that have been bent into a quarter-circle of radius R and length PI*R/2. His diagram is attached. Kleppner writes, "[t]he center of mass is halfway along the...

I know that, i studied it, but i can't actually make a picture in my mind, i can't really figure out why, i mean the forces and the torques are the same no? What's the big deal? What am i missing?

Homework Statement The system shown in (Figure 1) consists of two balls Aand B connected by a thin rod of negligible mass. Ball Ahas three times the inertia of ball B and the distance between the two balls is ℓ. The system has a translational velocity of v in the x direction and is spinning...

Homework Statement A massless rod of length L connects three iron masses. If the first mass (at x=0) has a mass of 1.90 kg and the second mass (at x=L) has a mass of 8.77 kg and the third mass (located at the center of mass of the system) has a mass of 148 kg, what is the moment of inertia I...

Why do we take the Center of mass to be on the right side rather than on the left? A uniform circular disc of radius 4a with a circular hole of radius 2a made in the disc. The mass of L is m and a particle of mass km is now fixed to L at the point P. The system is now suspended from the point S...

hello all, I am currently doing a lab investigating the relationship between the moment of inertia and speed. I have attached some pictures of my 'wheel' that is going to be rolled down a ramp. FYI i will be using a photogate to measure the time it takes the black strip to pass through...

A quick question, I remember my professor said to use the center of mass for solving the classic loop de loop problem. For example, he wanted us to use the distance from the surface of the loop to the center of the object (instead of just from the loop to the surface of the block) for the height...

Homework Statement We have a rod (length L, mass m) suspended at a point whose distance from the center of mass is a. 1) prove that (generally) there exist two values of a (a1, a2) for which the pendulum oscillates with the same period. 2) derive and explain: T = 2\pi\sqrt{\frac{a_1+ a_2}{g}}...

In planetary motion, the reduced mass of a system \mu is used in order to study the motion of the planet m in the non-inertial frame of the star M. Using \mu the trajectory of m turns out to be a conic. But this is the trajectory of the planet m as seen from the star M, correct? I read that in...

Homework Statement Consider a block placed on a surface, in two different configuration, a and b. Explain the condition for which the mass is in equilibrium and describe qualitatively the rotation it follows when it falls. Homework Equations Center of mass theorem \sum F = M a_{cm} The...

Homework Statement A quarter disc of radius 3 cm lies in the first quadrant. The areal density is (1.2 g/cm3)x + (0.7 g/cm3)y. Determine the mass of this object. Homework Equations The Attempt at a Solution For my bounds: x: 0 to 3 y: 0 to Sqrt[3 - x^2] When I took this integral I got...

Homework Statement Determine the center of mass in cylindrical coordinates of a cone with constant density ##\rho(\vec{r})##. (The cone is inverted, i.e. it's thinnest point is at ##z=0##.) Homework Equations ##m=\int\int\int_C \rho r \, drdzd\theta## ##\overline{r}=\int\int\int_C r\cdot r\...

Four 9.5 kg spheres are located at the corners of a square of side .60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other three. So, essentially my question is, why can I not use center of mass of the other 3 spheres to calculate the...

Homework Statement System S is static and is comprised of 3 identical metal pipes A, B and C which are placed so that A lays ontop of B and C. B lays into the y axis. The length of the pipes are orientated parallel with the z axis. The outer and inner radius of each pipe is (Outer : 0.51m)...

Homework Statement To determine the location of her center of mass, a physics student lies on a plank of weight 100.0 N and length 2.5 m supported by two scales 2.50 m apart. The left scale reads 420.0 N, and the right scale reads 210.0 N. (Note: Don’t neglect the weight of the plank when you...

Homework Statement For my physics lab, they had us do a simple static equilibrium experiment where we rested a ruler on a fulcrum (at its center of mass) and then attached varying amounts of weight on either end at different distances from the fulcrum. This screenshot is the data we recorded...

Hi, I'm currently learning about moments and equilibriums. I'm able to solve the problems quite properly, like determining different forces, distances and etc. what intrigued me is that when we say that an object has a moment of 1700 Nm about point o. Does it mean that the object will provide...

As far as I know in a system of particles or a body there is a point that behaves like all the forces on the system are applied at this point, but are these forces really applied in this point? Can you explain please, I thought at this and I arrived at the conclusion that these forces aren't...

Homework Statement A person with mass m is sitting on one end of a lifeboat of uniform density. Mass of lifeboat is 3m. The person then walks a distance of L to the other side of the lifeboat. Which of the following statements best characterizes the motion of the lifeboat? " The lifeboat...

Homework Statement A heavy ring of mass m is clamped on the periphery of a light circular disc. A small particle of equal mass is placed at the center of the disc. The system is rotated in such a way that the center moves in a circle of radius r and with a uniform speed v. Find the external...

I was reading about the ISS earlier, and this question came into my mind, and I can't seem to decided how this actually works. Here's the set-up: Say I have two masses stuck together (m1 and m2) to form a mass M in orbit around some planet (like the ISS, and some large space capsule that is...

Homework Statement I am after finding the centroid of the remaining area (hatched) when a circle is cut by a line. I made a diagram in CAD that demonstrates the problem. The idea is that, starting from the bottom of the circle, a cut is taken leaving a remaining shape whose area and...

Can anyone explain how to calculate the center of mass of a boat? and the centerline of a boat? Formulas, websites, anything helpful, just to let you know I haven't taken any high level physics classes so i don't know any of the fancy stuff lol. Thanks for the help

The facts are that the person is 183cm, 82kg, meaning his center of gravity is about at 105cm, he was running towards a railing of a balcony that is 108cm high, and allegedly hit the railing then fell over. Is this physically possible?

Homework Statement So this is just something i came up with to check if i am understanding everything allright, it all comes down to collisions in regard to the center of mass So two "masses" experience a glancing collision M1: vi - 3m/s (refered to as v1i) ; m - 2Kg (m1) M2...

Homework Statement There is an empty bottle described as an hollow cylinder, that lies on a paper. Now the paper is pulled with an acceleration a, so that the bottle starts rolling perfectly on the paper. (Have a look at the figure.) Homework Equations Calculate the acceleration of the center...

Homework Statement What is the moment of inertia of the 4 kg disk below when it rotates about the center of mass? The mass of the disk without the holes is 6 kg . Homework Equations Center of mass equation: (1/M)(∫xdm) Moment of inertia of a disk: I = 0.5mr2 Parallel axis theorem: I = Io +...

How would one go about finding the center of mass of a non-uniform rod when its cross-section has been modeling using a piecewise-defined function? For a specific case let's use a drumstick, noting its volume as a sum of half of a sphere (the 'butt' end), a cylinder (the 'shaft'), the majority...

Hello! If I pedal a bicycle, where is the force that moves the bike forward horizontally applied? Is it the bottom of the back wheel or the center of the back wheel? When the force applied to that point is F, does all that force goes into horizontal acceleration, or does some of that force go...

Homework Statement I need to find the final impact speed of the flame of a non-uniform candle. I am given that the mass per unit length increases linearly from top to bottom starting with 1kg/m at the bottom and 10kg/m at the top. I need to find how fast the candle flame is moving once the...

Find the coordinate of center of mass. Given: The quarter disk in the first quadrant bounded by x^2+y^2=4 I tried to solve this problem but can't figure out how to do it. so y integration limit is: 0 <= y <= sqrt(4-x^2)) x limit of integration: 0 <= x <= 2 and then after the dy integral I...

Homework Statement In a fireworks display a rocket is launched from the ground with a speed of 18.0m/s and a direction of 51.0 above the horizontal. During the flight, the rocket explodes into two pieces of equal mass. What horizontal distance from the launch point will the center of mass of...

Homework Statement Determine the position of the center of mass of a whole leg (a) when stretched out, and (b) when bent at 90°. Assume the person is 1.70 m tall. Homework Equations The Attempt at a Solution This is where I'm stuck...what's the mass? I doubt I can just use variable m because...

Apparently, a T-shaped organism in a positively curved space can wiggle around in such a way as to translate itself across space, thereby achieving locomotion simply by changing its shape in a specific series are ways. I've seen a computer generated animation of this and it's actually pretty...

Homework Statement Homework Equations Xcm = (x1m1+x2m2) / (m1+m2) The Attempt at a Solution ok so I'm having trouble understanding what's happening in the question... when the penguin moves, is the sled also moving? If it's friction less ice then if the penguins moves L, the sled will...

Homework Statement So we have a glass consisting of a 10 cm long cylinder on top of a 1 cm long bottom standing on a table. The radius is 3 cm. For every x in [0, 10] we let h(x) be the height of the center of mass when we fill the glass with x cm water. That is, h(x) is the distance from the...

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D = {(x, y) | 0 ≤ x ≤ 1, −1 ≤ y ≤ 1}; ρ(x, y) = 7xy2 I got my mass to be 7/3 but I'm not sure how to go about finding the center of mass

I think that the center of mass is not fixed in Relativity (unlike in classical physics). Could anyone look at my attached memo and tell me if I am right or wrong.

Homework Statement Homework EquationsThe Attempt at a Solution I think if I can locate the instantaneous axis of rotation ,then may be motion/velocity of CM could be determined . In the attached figure I have marked the two points A and B which are instantaneously at rest .The black arrows...

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...

Hi! I have been reading about the position of the center of mass in the Marion's Classical Dynamics book, in some point of the section he states that: "The location of center of mass of a body in uniquely defined, but the position vector R(of the center of mass ofcourse) depends on the...

Homework Statement 1.68 - ((51(0) + 109(1.5) + 66(3) + 13(0))/(51 + 66 + 109 + 13)) [/B] A person with mass m1 = 51 kg stands at the left end of a uniform beam with mass m2 = 109 kg and a length L = 3 m. Another person with mass m3 = 66 kg stands on the far right end of the beam and holds a...

I can't think of an instance of this in science fiction, but then I do not have the broadest knowledge of the field, so I could have missed something obvious to everyone else. I wonder, though, could a planet form at the center of mass of a binary star system or be captured there, and could...

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...