AP Physics 1 Momentum Review

Definition of Momentum

• Momentum (P): Product of mass and velocity.

  • Units: Kilograms (kg) times meters per second (m/s) or kg·m/s.

  • Linear Momentum: Specifically refers to momentum associated with linear motion.

Properties of Momentum

• Vector Quantity: Momentum has a direction; if velocity is positive, momentum is positive, and vice versa.

• Change in Momentum: Represented as ( \Delta P )

Conservation of Linear Momentum

• External Forces: Momentum changes when external forces act on the object.

  • Example: Pushing an object changes its momentum.

• Frictionless Acceleration: On a ramp, gravitational force acts as an external force, changing momentum as the object moves.

• Momentum Conservation: If no external forces act, linear momentum remains constant.

  • Written mathematically as: ( P_i = P_f )

Types of Collisions

• Elastic Collisions:

  • Momentum and kinetic energy are conserved.

  • Objects separate after collision.

    • Scenarios:

      • If masses are equal, one stops and the other moves.

      • If one mass is greater, both move with different speeds.

      • A heavier mass barely moves if struck by a lighter one.

• Inelastic Collisions:

  • Momentum is conserved, but kinetic energy is not.

  • Objects may stick together (perfectly inelastic).

• Momentum Equation: In elastic collisions: ( m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f} )

Force and Time Relationship

• Change in Momentum due to Force:

  • ( F_{average} \times \Delta T = \Delta P )

• Graphical Interpretation: Area under the force vs. time graph represents change in momentum.

Center of Mass and Motion

• Constant Velocity: Center of mass continues at constant speed if external forces are zero.

• Impulsive Forces: Internal forces do not affect momentum; only external forces change motion.

Special Situations

• Explosions: Momentum is conserved; even if objects move, their total momentum remains zero if initially at rest.

• Newton's Second Law:

  • Related to momentum as: ( F = \Delta P / \Delta T )

  • Change in momentum rewritten as: ( m \Delta V = \Delta P )

Key Takeaways

• Momentum Conservation: Vital in analyzing collision scenarios.

• Understand both collision types: Elastic (energy conserved) and inelastic (energy not conserved).

• Graphical Analysis: Important for finding changes in momentum and relationships.