Mechanics
Center of Mass (Two Objects)
The center of mass is the mass-weighted average position of a system.
Variables
x_cmm
Center of mass position
Position of center of mass
m₁kg
Mass 1
First object mass
x₁m
Position 1
Position of first object
m₂kg
Mass 2
Second object mass
x₂m
Position 2
Position of second object
Derivation
For a system of particles: x_cm = Σ(m_i × x_i) / Σm_i. For two objects, this simplifies to the weighted average.
Your notes
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Common questions
What is the Center of Mass (Two Objects) formula?
Center of Mass (Two Objects) is written xcₘ = m₁ x₁ + m₂ x₂/m₁ + m₂. The center of mass is the mass-weighted average position of a system. It belongs to Mechanics, under Dynamics.
What are the units in xcₘ = m₁ x₁ + m₂ x₂/m₁ + m₂?
In SI units, x_cm is center of mass position, measured in m; m₁ is mass 1, measured in kg; x₁ is position 1, measured in m; m₂ is mass 2, measured in kg; x₂ is position 2, measured in m.
How is the Center of Mass (Two Objects) formula derived?
For a system of particles: x_cm = Σ(m_i × x_i) / Σm_i. For two objects, this simplifies to the weighted average. The result is xcₘ = m₁ x₁ + m₂ x₂/m₁ + m₂.