Motion Of Center Of Mass Relative Motion And Reduced Mass
Concepts to Remember: Motion Of Center Of Mass Relative Motion And Reduced Mass
Motion of Center of Mass (CM) of a System of Particles:
 The center of mass of a system of particles is a point that represents the average position of the particles, weighted according to their masses.
Relative Motion:
 The motion of an object relative to another object is the motion of the object as observed from the frame of reference of the second object.
Reduced Mass:
 The reduced mass of a twoparticle system is a quantity that takes into account the masses of both particles and is used in calculations involving the relative motion of the particles.
Equation of Motion for the CM:
 The equation of motion for the CM of a system of particles is given by:
$$ \overrightarrow{F_{CM}}=M\overrightarrow{a_{CM}}$$ where:
 (\overrightarrow{F_{CM}}) is the net external force acting on the system of particles,
 (M) is the total mass of the system, and
 (\overrightarrow{a_{CM}}) is the acceleration of the CM.
Conservation of Momentum for the CM:
 The total momentum of a system of particles is conserved, meaning that it remains constant in the absence of external forces.
Collision in One Dimension:

When two objects collide along a straight line, the forces of collision act along that straight line.

Total momentum before collision = total momentum after collision

Total energy before collision = total energy after collision (only if the collision is elastic)
Concept of Impulse:

Impulse is the product of the net force acting on an object and the time interval during which the force acts.

Impulse causes a change in the momentum of the object.
Rocket Propulsion:

Rockets propel themselves forward by expelling hot gases in a backward direction.

The momentum of the system consisting of the rocket and its gas ejecta decreases backwards, according to Newton’s third law, but the momentum of the rocket itself increases forwards.