Center of mass Definition and 899 Threads

So I have been reading about conservation of linear momentum and conservation of angular momentum of a rotating object. For example a thin rod resting horizontally on the a flat surface. If this rod is being hit by a small object(collision), the rod will rotate about it's center of mass and will...

Homework Statement Using masses, springs a stop watch and ruler, determine the location of the center of mass and mass moment of inertia about an axis passing through the center of mass of a bicycle crank. The Attempt at a Solution I've been staring at this problem for a while now...

1. The density of part A (p)(kg/m^3) and in part B (p/2)(kg/m^3). Find the coordinate (x,y) of the center of mass of this object. (consider a piece of the object that is one meter in the z direction) 2. R = sum(m*r) / sum(m)...maybe? I am completely stumped on how to start this problem my...

so I am not too sure how to answer a question... ill word it the best i can: While doing an experiment where we use a Plumb Line and paper object and find the center of mass by letting the string (with mass attached to other end) hand and draw lines that eventually intersect at on specific...

Three Balls are moving along a straight line having the instantaneous positions shown in figure 8.15. At that instant, find the location and velocity of the center of mass of this system. Figure 8.15 Mass A---------------------Mass B-----------------------------------Mass C...

Homework Statement A uniform solid consist of a hemisphere of radius r and a right circular cone of base radius r fixed together so that their planes are coincident. If the solid can rest in equilibrium with any point of the curved surface of the hemisphere in contact with a horizontal plane...

Homework Statement Discuss when you can and can’t “pretend all the mass of an object is concentrated at the center of mass”. Homework Equations The Attempt at a Solution So I don't really understand what this is supposed to mean. I know that you utilize center of mass when trying...

Homework Statement A whimsical piece of furniture has the base shaped like a star. Formulate the condition in terms of the location of the center of mass of the object that the piece would not topple over. A sketch would be helpful. The Attempt at a Solution Can someone help me...

Homework Statement A uniform soda can of mass 0.140kg is 12.0cm tall and filled with 1.31kg of soda. Then small holes are drilled in the top and the bottom (with negligible loss of metal) to drain the soda. The can is placed upright such that the soda only drains from the bottom hole. What is...

A 500-kg cannon and a supply of 59 cannon balls, each with a mass of 19.0 kg, are inside a sealed railroad car with a mass of 50000 kg and a length of 41 m. The cannon fires to the right; the car recoils to the left. The cannon balls remain in the car after hitting the wall. After all the cannon...

Hi! :) This is my first post here, hoping this will help me understand a few things. I'm really stuck at this problem and it is annoying me because I think I understand the theory, but just can't seem to be able to do it. So any help, hints and tips to solve this kind of problem is highly...

Homework Statement ____ l _ l l_l l_l Find the y-coordinate of the center of mass. Each side l / _ is length a. I got an answer of 1.25a, but that isn't right. Homework Equations The Attempt at a Solution Area of each section * x-coordinate of center of mass. (the area...

Homework Statement Romeo (80.3 kg) entertains Juliet (58.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.73 m away from Juliet who is in the front of the boat. After the serenade, Juliet carefully moves to the rear of the boat (away from shore) to plant a kiss...

Homework Statement A man is standing at one end of a plank of length L = 10 m. The man has mass Mman = 100 kg and the plank has mass Mplank = 40 kg and the plank is atop a frictionless sheet of ice. At the other end of the plank sits a large rock of mass Mrock = 200 kg. The center of mass of...

Homework Statement A nonuniform bar is suspended at rest in a horizontal position by two massless cords as shown in Fig. 12-45. One cord makes the angle θ = 15.5° with the vertical; the other makes the angle φ = 58.5° with the vertical. If the length L of the bar is 6.08 m, compute the...

A thin rectangular plate of uniform areal density σ = 3.13 kg/m2 has length of 44.0 cm and width of 26.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis. There is a circular hole of radius 7.00 cm with center at (x,y) = (16.00,11.00) cm...

Homework Statement A thin rectangular plate of uniform areal density σ = 3.06 kg/m2 has length of 37.0 cm and width of 25.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis. There is a circular hole of radius 6.50 cm with center at...

1. A straight rod has one end at the origin and the other end at the point (L,0) and a linear density given by \lambda=ax^2, where a is a known constant and x is the x coordinate. Since this wire is not uniform, you will have to use integrtation to solve this part. Use M=\int_0^L dm to find the...

Hi! I'm trying to understand the concept of the center of mass. I know the center of mass is the point within the object where it could be considered that the entire mass of the object lies, thus forces are going through this center, but how is it possible that the center of mass could move...

Homework Statement https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-09-Momentum/plate_with_hole/3.gif A uniform circular plate of radius 11 cm has a circular hole of radius 3 cm cut out of it. The center of the plate is at the origin...

Homework Statement Richard, mass 80 kg, and Judy, who is less massive, are enjoying Lake George at dusk in a 30 kg canoe. When the canoe is at rest in the placid water, they change seats, which are 3.0 m apart and symmetrically located with respect to the canoe's center. Richard notices that...

Homework Statement Figure 7-29 shows a composite slab with dimensions 22.0 cm multiplied by 13.0 cm multiplied by 2.8 cm. Half of the slab is made of aluminum (density = 2.70 g/cm3) and half of iron (density = 7.85 g/cm3), as shown. How far from the line joining the two metals is the center...

The center of mass between two equally sized planets would be right in the center. When you find the center of mass between the Earth and a satellite how would I find the distance offset from the hypothetical midpoint of the earth? The Earth contributes more to the center of mass when paired...

Homework Statement A club-axe consists of a symmetrical 16.0 kg stone attached to the end of a uniform 1.6 kg stick, as shown in the figure. The length of the handle is L1 = 71.0 cm and the length of the stone is L2 = 16.0 cm. How far is the center of mass from the handle end of the club-axe...

Homework Statement http://img35.imageshack.us/img35/6177/uthw404.jpg Homework Equations The Attempt at a Solution I tried finding the center of mass of the square as if there were no hole in it, and then I added the radius of the circle to the x-coordinate of that. It's wrong...

Studying for a test and I can't really grasp a full example problem. I would also like help on a couple further example problems that are not done for me. Homework Statement Find the exact coordinates of the centriod: a. y=4-x^2, y=0 b. 3x+2y=6, y=0, x=0 c. y=e^x, y=0, x=0, x=1 d...

Homework Statement A rod of length 30.0 cm has linear density (mass-per-length) given by λ = 50.0 g/m + 20.0x g/m2 where x is the distance from one end, measured in meters. (a) What is the mass of the rod? (b) How far from the x = 0 end is the center of mass? Homework...

Homework Statement The attached jpeg shows a force plate with four measured masses each corresponding to a corner node. Calculate the center of mass on the force plate. Homework Equations I think they would be: xcg = (x1M1 + x2M2 + x2M3 + x4M4) / (M1 + M2 + M3 + M4) The ycg...

I guess this is a relatively simple question, but depending on the answer can have complex follow-up questions. So here goes with the first: is there a center of mass to the universe? Or is this not possible? P.S. Is this site being weird for anyone? It only works on my phone's web browser...

Homework Statement There is an arc with an angle of 2\alpha and radius R What is its center of mass. (It is implied that it is to be measured from the center of the circle the arc is a part of.Homework Equations Integration, trigonometry.The Attempt at a Solution Well, the formula for a center...

The center of mass of the Earth is approximately at the center. The center of mass is also where the force vector of the gravitational force is pointing. (down that is). Now the total gravitational force excerted on me should be the sum of the force excerted by the Earth plus anything else...

can some one explain me why,center of mass of an object can lie outside the surface of the object also?

Homework Statement Find x coordinant of the the center of mass point of a uniform wire that subtends an arc of 22 degrees if the radius of the circular arc is 1m. Homework Equations I begin with: length = r*theta Therefore M = density*r*theta dm = density*ds = denisty*r8*d(alpha)...

Homework Statement A bowling ball with Mass M and Radius R is thrown down an alley so that the balls center of mass has an initial horizontal velocity of Vo and the ball is not rotating. Kinetic friction force is f^k. Find: a) an expression for the acceleration and velocity of the...

Homework Statement A 1.90 kg box slides down a rough incline plane from a height h of 1.51 m. The box had a speed of 2.99 m/s at the top and a speed of 2.56 m/s at the bottom. Calculate the mechanical energy lost due to friction (as heat, etc.).

I needed to refresh my classical physics knowledge and I was going through Prof. Walter Lewin's physics videos at ocw.mit.edu and at some point he proposed the following theorem without proof: "The angular momentum due to rotation about the center of mass is universal and does not depend on...

Homework Statement A uniform circular plate of radius 14 cm has a circular hole of radius 2 cm cut out of it. The center of the plate is at the origin of the coordinate system and the center of the hole is located along the x-axis a distance 4 cm from the origin. What is the position of the...

[b]1. Homework Statement Calculate the time the moon rotates once around the earth, and show that you have to add 4 hours to that since the moon & the Earth rotate around their center of mass. hint: use the reduced mass: \overline{m}=\frac{m_{1}m_{2}}{m_{1}+m_{2}} mass of moon...

1. A uniform meter stick is pivoted at its center. The meter stick has a M1 = 103 g mass suspended at the D1 = 28 cm position. Which is measured from the left end. At what position should a M2 = 74 g mass be suspended to put the system in equilibrium? Give your answer D2 in cm from the left end...

What is the correct formula for center of mass of a binary system? I had seen that it is R=\frac{m_{1}r_{1}+m_{2}r_{2}}{m_{1}+m_{2}} If that is the right equations what exactly does r one and two stand for? I had also seen a much more complicated formula. Side note: This is not...

Homework Statement A(n) 64 kg boat that is 8 m in length is initially 8.5 m from the pier. A 32 kg child stands at the end of the boat closest to the pier. The child then notices a turtle on a rock at the far end of the boat and proceeds to walk to the far end of the boat to observe the...

Homework Statement Let D be the region in the (x, y) plane bounded by the lines y=x, y=4x and the hyperboals xy=1 and xy=9. find the center of mass of D. Homework Equations The Attempt at a Solution My thought: to use the center of mass formula? and use the change of variables?

center of mass and "center of energy" Hi everyone, I recently came across a little thought experiment in a book that seemed to imply that the center of mass of an isolated system is not a strictly conserved quantity. Rather, it is the "center of energy" that remains fixed. The idea of a...

How would I find the center of mass (COM) for a ring of variable density, where the variation in density can be described by a continuous mathematical equation. The density at each location along the ring is described by a function (d) whose independent variables are radius (r) and angle...

Homework Statement Find the center of mass of the triangle with vertices at (0,0), (6,6) and (-6,6) if the density at (x,y) is equal to y. Homework Equations The Attempt at a Solution I am having trouble with these centroid/center of mass problems, and I can't even figure out the...

1. There are two 50 kg skaters in a friction-less horizontal surface. Both have velocities of |V|=10 m/s, in opossite directions (that is, skater 1's velocity is 10 m/s i, while skater 2's velocity is -10 m/s i). They both skate parallel to each other with a distance of 1,5m. Skater 1 has a...

Homework Statement A lamina has the shape of the region in the first quadrant that is bounded by the graphs of y = sinx and y= cosx, between x = 0 and x = π/4. Find the centre of mass if the density is δ(x,y) = y. Homework Equations I know all the equations for moments and center of...

OMG second time I'm opening a thread in the wrong forum FFS! Damn bookmarks! MODS move it please. Homework Statement Not a home work question, just something i cam across and need a clarification. Could One show me how to derive to the equation that X(cm)=int(X dm)/M int=the deformed S of the...

Homework Statement a solid in the first octant is bounded by the planes y=0 and z=0 and by the surfaces z=4-x^2 and x=y^2. its density function =kxy, k is a constant. find the mass of the solid and the center of mass Homework Equations My= double integral of D[x*kxy]dA Mx=double...

Homework Statement Given: g=9.8 m/ss Given: A uniform flexible chain whose mass is 7 kg and length is 5 m. Given: A small frictionless pulley whose circumference is negligible compared to the length of the chain. Problem: Initially the chain is hung over the pulley with nearly equal...