4.3 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.
  • 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. BOUNDARY STATEMENT AP Physics 1 includes a quantitative and qualitative treatment of conservation of momentum in one dimension and a semiquantitative treatment of conservation of momentum in two dimensions. Exam questions involving solution of simultaneous equations are not included in AP Physics 1, but the AP Physics 1 Exam may include questions that assess whether students can set up the equations properly and reason about how changing a given mass, speed, or angle would affect other quantities. AP Physics 2 includes a full treatment of conservation of momentum in two dimensions for problems that include one unknown final velocity. | AP Physics 1: Algebra-Based Course and Exam Description

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. 84 Linear Momentum UNIT 4 TOPIC 4.4 Elastic and Inelastic Collisions