Mathematical formulas

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Subjects
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

r_{CM} = \frac{\sum _{i} m _{i} r _{i}}{\sum _{i} m _{i}}

For a continuous distribution

r_{CM} = \frac{1}{M} \int r d m

Related formulas

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Center-of-mass velocity
$v_{CM} = \frac{\sum _{i} m _{i} v _{i}}{M} = \frac{P _{total}}{M}$
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Rolling without slipping
$v_{CM} = R ω$
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