# Classical mechanics-coordinates

1. May 12, 2013

1. The problem statement, all variables and given/known data

Attached is the picture of a dumbbell. I do not understand how the coordinate of M1 is
M2 R/ (M1 + M2)

It is not an assignment question but an example from a book.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. May 12, 2013

### ehild

The origin is at the centre of mass. You certainly know how to determine the position of the CM?

ehild

3. May 12, 2013

CM= (R1m1+R2M2)/M1+M2
because CM=0, I get M1 R1 = -R2 M2
which further gives me
R1= RM2 / (M2-M1)

=|

4. May 12, 2013

### ehild

What do you mean on R1 and R2? If they are coordinates of the spheres with respect to the CM, the formula is correct, but use parentheses. (R1m1+R2M2)/(M1+M2)=0

How are R1 and R2 related to the distance R between the spheres?

ehild

5. May 12, 2013

R= R_1 + R_2
where R_i is the distance to M_i from CM.

6. May 12, 2013

In the book R_1 = R M2/ (M1 + M2) but mine is R1= R M2 / (M2-M1)

7. May 12, 2013

### ehild

If x1, x2 are coordinates of m1, m2, respectively, the x coordinate of the CM is (x1m1+
x2m2)/(m1+m2).
If they are distances from the CM, the coordinate of m2 is negative: m1R1-M2R2=0

ehild

Last edited: May 12, 2013