So far we have studied the motion of single bodies. But when a system is made up of several objects — fragments of an explosion, planets in a solar system, billiard balls colliding — there is a special point that summarises its overall behaviour: the centre of mass. This chapter defines it as the weighted average of positions, studies its velocity and Newton’s second law, the quantities it summarises, the anti-matter method for bodies with holes, König’s decomposition of kinetic energy and angular momentum, and introduces the moment of a force and rigid-body equilibrium.
Sections
- Definition and calculation of the CM
- Galilean composition of velocities
- Newton’s second law for the CM
- The properties summarised in the centre of mass
- The anti-matter method
- Gravitational potential energy of the CM
- Decomposition of kinetic energy
- Moment of a force (torque)
- Angular momentum