Overview
This lecture introduces the concepts of momentum and impulse in physics, covering key definitions, formulas, and the impulse-momentum theorem.
Momentum: Definition and Basic Concepts
- Momentum (symbol: p) is defined as the product of mass (m) and velocity (v): p = m × v.
- Momentum is a vector quantity, having both magnitude and direction (same as velocity).
- Momentum is fundamental in the study of dynamics of material points.
Newton’s Second Law and Momentum
- Newton’s second law states that force (F) equals mass times acceleration: F = m × a.
- If mass varies, force can be expressed as the time derivative of momentum: F = dp/dt.
- The change in momentum over time relates directly to the applied force.
Impulse and the Impulse-Momentum Theorem
- Impulse (J) is defined as the product of force (F) and the time interval (Δt) it acts: J = F × Δt (for constant force).
- Impulse is also equal to the change in momentum: J = Δp = p_final – p_initial.
- The units of impulse are Newton-seconds (N·s).
- Integrating force over time gives impulse for varying forces.
Application and Integration
- To find total impulse when force varies, integrate force over the time interval: J = ∫ F dt.
- The impulse-momentum theorem links the impulse delivered to an object to its change in momentum.
Key Terms & Definitions
- Momentum (p) — Product of an object's mass and velocity (p = m × v); a vector quantity.
- Impulse (J) — The change in momentum; calculated as force times the duration it acts (J = F × Δt).
- Newton's Second Law — States that force equals the derivative of momentum with respect to time (F = dp/dt).
Action Items / Next Steps
- Review the impulse-momentum theorem and related formulas.
- Prepare for upcoming lessons by ensuring understanding of momentum and impulse.
- Visit the provided course website for related articles and further exercises if needed.