# Finding center of mass of three disks

1. Oct 28, 2014

### CaptainOfSmug

1. The problem statement, all variables and given/known data
All three disks are made of sheet metal of the same material, and the diameters are 1.2m ,2.4m , and3.6m . Assume that the x-axis has its origin at the left-most point of the left-most object and it points to the right.
A)
Determine the location of the center of mass of the system

B)
Repeat the calculation for three solid spheres all made of the same metal and having the same diameters as in part A.

2. Relevant equations
cm=m1r1+m2r2...etc /m1+m2...etc

3. The attempt at a solution
Now I know this is most likely a very simple problem but using my formulas I'm given doesn't seem to work for me, so I know I am setting up this wrong. I guess I need help with the whole concept of center of mass, just from assumption I know the center of mass will be between 2.4cm and 3.6cm and I know the diameters are all increasing by 1.2cm, however when I plug and chug my formula I realized all I'm doing is taking the average which cannot be true for this (I'm assuming). So I'm guessing I'm having trouble with the reference frames and figuring out the inertial values...

I'm not looking for a handout answer but I do need to understand this concept, thanks in advance!
Cheers!

2. Oct 28, 2014

### SteamKing

Staff Emeritus
We really can't comment on what you're doing wrong unless you post your calculations.

3. Oct 29, 2014

### CaptainOfSmug

Well I'm at a loss of how to even begin my calculations, I'm having trouble with how to approach the problem, my book isn't doing very well on this topic for me and my professor is essentially a proctor for tests, I tried khan academy with little luck. Should I be setting up three reference frames then each in accordance of each disk? I have no idea how to find the inertia of each disk so I assumed I just leave them as m1,m2, and m3 but I'm assuming there mass increases proportionally to their size since they are the same material, and each disk increases diameter by 1.2cm. So for the relevant equation I gave I assume the denominator will be 6m, but I'm having trouble with the numerator.

EDIT:
So here's what I've come if so far but I'm not sure if it's right:
center of mass= m1x1+2m2x2+3m3x3 /6m
=2.8cm. This answer seems somewhat reasonable, but my intuition tells me it should be larger

Last edited: Oct 29, 2014
4. Oct 29, 2014

### Orodruin

Staff Emeritus
Your problem statement mentions nothing of the location of the objects apart from the left most one. Is this the problem exactly as stated?

What is the mass of a solid disk? Where are the disk centers located?

5. Oct 29, 2014

### SteamKing

Staff Emeritus
I think I can see one problem right off the bat. The disks are supposed to have diameters which increase in the progression 1.2 m, 2.4 m, and 3.6 m, yet in your formula for the center of the mass, you are assuming that if the mass of the smallest disk is m, then the mass of the next larger disk is 2m, and the mass of the largest disk is 3m. This is incorrect.

Since the OP states that all three disks are made of sheet metal and are the same material, it would then be reasonable to assume that all three disks have the same thickness. This implies that the mass of each disk varies as the volume of metal in the disk, which, since each disk has the same thickness, also implies that the mass of each disk is proportional to the area of the disk. Since the area of the disk is in turn proportional to the square of the diameter, then the mass of each disk does not increase as the ratio of the diameters, but as the ratio of the square of the diameters.

The OP seems to imply that each disk is laid down in a line, with the smaller disk touching, but not overlapping, the next larger disk located to its right.

A simple sketch should be made showing three disks laid out thus: oO∅. Using this sketch, one can then determine where the center of mass of each disk is in relation to the origin, which the OP states is located at the leftmost point of the leftmost disk. Once the proper mass relationship and the location of the center of each disk is determined, then you may apply the formula to determine the center of mass of the three disks.

For part B of the problem, rinse and repeat the procedure above, except instead of disks, use spheres instead. (Hint: there will be a different relationship between each mass in the case of spheres as opposed to disks made out of sheet metal.)

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