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 two-particle 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.