MOMENTUM

Momentum is a fundamental concept in physics that describes the motion of an object. Below is a breakdown of all key concepts related to momentum:


1. Linear Momentum

  • Definition: Linear momentum is the product of an object’s mass and velocity.
  • Formula: p=mv where:
    • p: Momentum (vector quantity)
    • m: Mass of the object (scalar quantity)
    • v: Velocity of the object (vector quantity)
  • SI Unit: kgm/s

2. Conservation of Momentum

  • Principle: In an isolated system (no external forces), the total momentum remains constant.
  • Formula: ∑pinitial ​= ∑pfinal​
  • Applications:
    • Collisions (elastic and inelastic)
    • Explosions

3. Impulse

  • Definition: Impulse is the change in momentum caused by a force acting over a period of time.
  • Formula: J=Δp=F⋅Δt where:
    • J: Impulse
    • Δp: Change in momentum
    • F: Force applied
    • Δt: Time duration
  • SI Unit: Ns (Newton-second), which is equivalent to kgm/s.

4. Types of Collisions

  • Elastic Collisions:
    • Kinetic energy and momentum are conserved.
    • Objects bounce off each other without deformation or heat generation.
  • Inelastic Collisions:
    • Momentum is conserved, but kinetic energy is not.
    • Objects may stick together or deform after collision.
  • Perfectly Inelastic Collision:
    • A special case where objects stick together after collision.

5. Center of Mass and Momentum

  • The momentum of a system of particles is the product of the total mass and the velocity of the center of mass: Ptotal​=MVCM​​ where:
    • Ptotal​: Total momentum of the system
    • M: Total mass of the system
    • VCM​: Velocity of the center of mass

6. Angular Momentum

  • Definition: Angular momentum is the rotational equivalent of linear momentum.
  • Formula: L=r×p where:
    • L: Angular momentum (vector)
    • r: Position vector
    • p: Linear momentum
  • For a rotating rigid body: L= Iω where:
    • I: Moment of inertia
    • ω: Angular velocity
  • Conservation of Angular Momentum:
    • Linitial ​= Lfinal

7. Relativistic Momentum

  • At speeds close to the speed of light, momentum is adjusted using the Lorentz factor:
    • p=  ​​mv​ (1 – v2/c2)1/2 where:
      • c: Speed of light in a vacuum (3×108 m/s)

8. Practical Examples of Momentum

  • Sports (e.g., catching or hitting a ball)
  • Vehicle collisions (analyzing crash dynamics)
  • Rockets and propulsion (conservation of momentum in space)
  • Conservation laws in particle physics.

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