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Physics · Glossary

What is Center of mass; momentum of a system?

Definition 19.1 University Physics — Year 1 · Chapter 19 — Systems of Points; Introduction to Rigid Bodies

For particles of masses mim_i at MiM_i, total mass M=∑miM = \sum m_i, the center of mass (barycenter) GG is defined by

∑imi GMi→=0→,i.e.OG→=1M∑imi OMi→\sum_i m_i\,\vect{GM_i} = \vect 0, \qquad\text{i.e.}\qquad \vect{OG} = \frac{1}{M}\sum_i m_i\,\vect{OM_i}

for any origin OO. The momentum of the system is P→=∑imiv→i=Mv→G\vect P = \sum_i m_i\vect v_i = M\vect v_G.

Examples

Example 19.3 (Diver, recoil, collision)

The diver’s GG follows a parabola under her weight alone, however she twists — her muscles are internal forces. A rifle of 4.0 kg4.0\,\mathrm{kg} firing a 10 g10\,\mathrm{g} bullet at 800 m/s800\,\mathrm{m}/\mathrm{s}: P→=0→\vect P = \vect 0 before and after, so the rifle recoils at 2.0 m/s2.0\,\mathrm{m}/\mathrm{s}. Two cars, 1000 kg1000\,\mathrm{kg} at 20 m/s20\,\mathrm{m}/\mathrm{s} and 1500 kg1500\,\mathrm{kg} at rest, that lock together: v=20000/2500=8.0 m/sv = 20000/2500 = 8.0\,\mathrm{m}/\mathrm{s} — momentum conserved, while 60%60\% of the kinetic energy has gone into crumpled metal and heat. Momentum is conserved in every collision; kinetic energy only in elastic ones (Exercise 19.12).

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