# Classical mechanics-coordinates

## Homework Statement

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.

## The Attempt at a Solution

#### Attachments

• newdoc.pdf
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ehild
Homework Helper
The origin is at the centre of mass. You certainly know how to determine the position of the CM?

ehild

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

=|

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

=|

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

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

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

ehild
Homework Helper
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

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