Lecture Notes: Impulse and Momentum

Key Concepts

• Conservation Laws

  • Conservation of Matter: Known from chemistry.
  • Conservation of Energy: Known from physics.
  • Conservation of Momentum: Extends the concept to momentum.

• Momentum (p)

  • Defined as the product of mass and velocity.
  • Momentum is a vector quantity.
  • SI Units: kilograms meters per second (kg·m/s).
  • Affects how difficult it is to stop a moving object.
  • Examples:
    • A rolling ball gathers momentum downhill.
    • A massive object or a fast-moving object has a larger momentum.

Momentum in Practice

• Car in Motion

  • Momentum = mass × velocity.
  • Braking involves force applied over time to stop the car.
  • Greater mass/velocity requires more force over time to stop.

• Impulse

  • Defined as force applied over a duration of time.
  • Measured in Newton seconds (N·s).

Impulse-Momentum Theorem

• States that impulse (force × time) is equal to the change in momentum (Δp).
• Expressed as f Δt = Δp or mv(final) - mv(initial).
• Relationship to momentum:
  • Gain in momentum: Object receives force over time.
  • Loss in momentum: Object imparts force elsewhere over time.
• Similar to the work-energy theorem for conservation of energy.

Applications and Ramifications

• Impact Forces

  • Instantaneous impact results in a large force.
  • Prolonged impact duration results in a smaller force.
  • Example: Falling onto a trampoline vs. hard ground.

• Sports Application

  • Baseball players swing through the ball to maximize force applied by maintaining contact longer.

Conservation of Momentum

• In collisions, total momentum is conserved.
• Before and after collision, the sum of momenta of the objects remains the same.
• Example: Pool table balls.
  • One ball's momentum is transferred to another upon collision.

Next Steps

• More discussions on collisions in the subsequent tutorial.

---

Stay tuned for more tutorials, support content creation via Patreon, and feel free to reach out via email.