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The Centre of Mass Calculator will calculate:

- Centre of mass of a system composed by two distant objects in one dimension
- Centre of mass of a system composed by three non-collinear distant objects in three dimensions.

The centre of mass of a system composed by two distant objects in one dimension is m |

The centre of mass of a system composed by three distant non-collinear objects in three dimensions is m |

The centre of mass of a system composed by two distant objects in one dimension calculations |
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x_{C} = x_{1} × m_{1} + x_{2} × m_{2}/m_{1} + m_{2}x _{C} = × + × / + x _{C} = /x _{C} = |

The centre of mass of a system composed by three distant non-collinear objects in three dimensions calculations |

r_{C} = √(x_{1} × m_{1} + x_{2} × m_{2} + x_{3} × m_{3})^{2}+ (y_{1} × m_{1} + y_{2} × m_{2} + y_{3} × m_{3} )^{2}+ (z_{1} × m_{1} + z_{2} × m_{2} + z_{3} × m_{3})^{2}/m_{1} + m_{2} + m_{3}r _{C} = √( × + × + × )^{2}+ ( × + × + × )^{2}+ ( × + × + × )^{2}/ + + r _{C} = √()^{2}+ ()^{2}+ ()^{2}/r _{C} = √/r _{C} = √/r _{C} = /r _{C} = |

Centre of Mass Calculator Input Values |

mass of the first object (m_{1}) kg |

mass of the second object (m_{2}) kg |

mass of the third object (m_{3}) kg |

x-position of the first object (x_{1}) m |

x-position of the second object (x_{2}) m |

x-position of the third object (x_{3}) m |

y-position of the first object (y_{1}) m |

y-position of the second object (y_{2}) m |

y-position of the third object (y_{3}) m |

z-position of the first object (z_{1}) m |

z-position of the second object (z_{2}) m |

z-position of the third object (z_{3}) m |

Please note that the formula for each calculation along with detailed calculations are available below. As you enter the specific factors of each centre of mass calculation, the Centre Of Mass Calculator will automatically calculate the results and update the Physics formula elements with each element of the centre of mass calculation. You can then email or print this centre of mass calculation as required for later use.

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Please note the following guidance when using the Buoyancy Calculator to comlpete specific buoyancy calculations:

**When calculating the centre of mass of a system composed by two distant objects in one dimension:**If no coordinates are available and you only know the linear distance between the centres of mass of the two objects, use 0 as the value for x_{1}and the value of the given distance for x_{2}. The result provides the distance of system's centre of mass from the first object.**When calculating the centre of mass of a system composed by three distant non-collinear objects in three dimensions:**If there are only two objects available, please leave the box of the third mass (m_{3}) empty. Also, if there are only two dimensions available, please leave the values of the third coordinate empty (z_{1}, z_{2}and z_{3}).

x_{C} = *x*_{1} × m_{1} + x_{2} × m_{2}*/**m*_{1} + m_{2}

r_{C} = *√*__(x___{1} × m_{1} + x_{2}∙m_{2} + x_{3}∙m_{3} )^{2}__+ (y___{1} × m_{1} + y_{2} × m_{2} + y_{3} × m_{3} )^{2}__+ (z___{1} × m_{1} + z_{2}∙m_{2} + z_{3} × m_{3} )^{2}*/**m*_{1} + m_{2} + m_{3}

The following Physics tutorials are provided within the Centre of Mass and Linear Momentum section of our Free Physics Tutorials. Each Centre of Mass and Linear Momentum tutorial includes detailed Centre of Mass and Linear Momentum formula and example of how to calculate and resolve specific Centre of Mass and Linear Momentum questions and problems. At the end of each Centre of Mass and Linear Momentum tutorial you will find Centre of Mass and Linear Momentum revision questions with a hidden answer that reveals when clicked. This allows you to learn about Centre of Mass and Linear Momentum and test your knowledge of Physics by answering the test questions on Centre of Mass and Linear Momentum.

- 6.1 - Centre of Mass. Types of Equilibrium
- 6.2 - Determining the Centre of Mass in Objects and Systems of Objects
- 6.3 - Newton's Second Law for System of Particles
- 6.4 - Moment of Force. Conditions of Equilibrium
- 6.5 - Linear Momentum
- 6.6 - Collision and Impulse. Types of Collision
- 6.7 - Law of Conservation of Momentum and Kinetic Energy
- 6.8 - Momentum and Impulse in Two Dimensions. Explosions.
- 6.9 - Torque

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