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4.3 Conservation of Linear Momentum

Syllabus
2024
Topic
4.3
Level
—

Learning objectives

4.3A—Describe the behavior of a system using conservation of linear momentumDescribe the behavior of a system using conservation of linear momentum.• A collection of objects with individual momenta can be described as one system with one center-of-mass velocity.- i. For a collection of objects, the velocity of a system’s center of mass can be calculated using the equation- ii. The velocity of a system’s center of mass is constant in the absence of a net external force.• The total momentum of a system is the sum of the momenta of the system’s constituent parts.• In the absence of net external forces, any change to the momentum of an object within a system must be balanced by an equivalent and opposite change of momentum elsewhere within the system. Any change to the momentum of a system is due to a transfer of momentum between the system and its surroundings.- i. The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. This is a direct result of Newton’s third law. TOPIC 4.3 Conservation of Linear Momentum- ii. A system may be selected so that the total momentum of that system is constant.- iii. If the total momentum of a system changes, that change will be equivalent to the impulse exerted on the system. Relevant equation:• Correct application of conservation of momentum can be used to determine the velocity of a system immediately before and immediately after collisions or explosions.4.3B—Describe how the selection of a system determines whether the momentum of that system changesDescribe how the selection of a system determines whether the momentum of that system changes.• Momentum is conserved in all interactions.• If the net external force on the selected system is zero, the total momentum of the system is constant.• If the net external force on the selected system is nonzero, momentum is transferred between the system and the environment. BOUNDARY STATEMENT AP Physics C: Mechanics only expects students to quantitatively analyze collisions and interactions in one or two dimensions. Three-dimensional collisions may be analyzed qualitatively.

4.3.A—Describe the behavior of a system using conservation of linear momentum

Describe the behavior of a system using conservation of linear momentum.

  • A collection of objects with individual momenta can be described as one system with one center-of-mass velocity.
    • i. For a collection of objects, the velocity of a system’s center of mass can be calculated using the equation
    • ii. The velocity of a system’s center of mass is constant in the absence of a net external force.
  • The total momentum of a system is the sum of the momenta of the system’s constituent parts.
  • In the absence of net external forces, any change to the momentum of an object within a system must be balanced by an equivalent and opposite change of momentum elsewhere within the system. Any change to the momentum of a system is due to a transfer of momentum between the system and its surroundings.
    • i. The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. This is a direct result of Newton’s third law. TOPIC 4.3 Conservation of Linear Momentum
    • ii. A system may be selected so that the total momentum of that system is constant.
    • iii. If the total momentum of a system changes, that change will be equivalent to the impulse exerted on the system. Relevant equation:
  • Correct application of conservation of momentum can be used to determine the velocity of a system immediately before and immediately after collisions or explosions.

4.3.B—Describe how the selection of a system determines whether the momentum of that system changes

Describe how the selection of a system determines whether the momentum of that system changes.

  • Momentum is conserved in all interactions.
  • If the net external force on the selected system is zero, the total momentum of the system is constant.
  • If the net external force on the selected system is nonzero, momentum is transferred between the system and the environment. BOUNDARY STATEMENT AP Physics C: Mechanics only expects students to quantitatively analyze collisions and interactions in one or two dimensions. Three-dimensional collisions may be analyzed qualitatively.