Center of Mass (Two Objects)
The center of mass is the mass-weighted average position of a system.
Variables
Derivation
For a system of particles: x_cm = Σ(m_i × x_i) / Σm_i. For two objects, this simplifies to the weighted average.
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Check value
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- m₁ = 2 kg (Mass 1)
- x₁ = 3 m (Position 1)
- m₂ = 4 kg (Mass 2)
- x₂ = 5 m (Position 2)
Result: xcm = 4.3333333 m
Other mechanics formulas with the same quantities
- Universal Gravitation (Gravitation) shares Mass 1, Mass 2
- Gravitational Potential Energy (General) (Gravitation) shares Mass 1, Mass 2
Where this formula is listed
- Mechanics formulas, under Dynamics, alongside Newton's Second Law, Weight, Friction Force, Hooke's Law and Drag Force.
- In the mechanics list it comes after Terminal Velocity and before Pressure.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Center of Mass (Two Objects) formula?
Center of Mass (Two Objects) is written x_cm = (m₁x₁ + m₂x₂)/(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 x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂)?
In SI units, x_c m 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 x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂).