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:

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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

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2. Conservation of Momentum

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

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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.

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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.

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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: P_total​=MV_CM​​ where:
  • P_total​: Total momentum of the system
  • M: Total mass of the system
  • V_CM​: Velocity of the center of mass

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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:
  • L_initial ​= L_final​​

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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)

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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.