Centre of Mass of Two Bodies
Centre of Mass of Two Bodies
The centre of mass is the mass-weighted average position — the point a system balances about and moves as if all mass were concentrated there.
It is x_c = (m_1·x_1 + m_2·x_2)/(m_1 + m_2). where m_1, x_1 and m_2, x_2 are the two masses and their positions.
Inputs
m_1 := 3 kg=3 kg
x_1 := 0 m=0 mm
m_2 := 5 kg=5 kg
x_2 := 2 m=2 m
Take the mass-weighted average position.
x_c := (m_1·x_1 + m_2·x_2)/(m_1 + m_2)=1.25 m
Results
The centre of mass lies closer to the heavier body. It extends to many bodies and to 2-D/3-D by averaging each coordinate.
Assumptions & limitations
- Point masses on a line.
- Positions on a common axis.
- Rigid arrangement.