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Basic Physics
Linear momentum, impulse and collisions
Center of mass

7. Linear momentum, impulse and collisions

Center of mass

In 7. Linear momentum, impulse and collisions

Formula

\vec r_{\text{CM}} = \frac{\sum_i m_i\vec r_i}{\sum_i m_i}

For a continuous distribution

\vec r_{\text{CM}}=\frac{1}{M}\int\vec r\,dm

Tags

collisions
Continuity
physics
physics formula
momentum
momentum impulse collisions

Detail

The center of mass is the mass-weighted average of the positions.

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Related formulas

Related
Center-of-mass velocity
$\vec v_{\text{CM}}= \frac{\sum_i m_i\vec v_i}{M} = \frac{\vec P_{\text{total}}}{M}$
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Rolling without slipping
$v_{\text{CM}}=R\omega$
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