During a collision in an isolated system, which statement about momentum is true?

During a collision in an isolated system, which statement about momentum is true?

• A. The momentum of each individual object remains the same.
• B. The momentum of the system increases.
• C. Momentum is not involved in collisions.
• D. The total momentum of the system remains constant.

Answer: (D)

Momentum is conserved in an isolated system because there are no external impulses acting on it. During a collision, the forces between the objects are internal and are equal and opposite, so they can change the individual momenta of the objects, but the vector sum of all momenta in the system stays the same. Before the collision, p_total equals the sum of the individual momenta; after the collision, the individual momenta may differ, but they add up to the same total. For example, two skaters pushing off each other swap momentum between them, yet the total momentum of the pair remains constant. External forces would introduce an external impulse and could change the total momentum, but in an isolated collision that external influence is absent, so the total momentum remains constant.

Momentum is conserved in an isolated system because there are no external impulses acting on it. During a collision, the forces between the objects are internal and are equal and opposite, so they can change the individual momenta of the objects, but the vector sum of all momenta in the system stays the same. Before the collision, p_total equals the sum of the individual momenta; after the collision, the individual momenta may differ, but they add up to the same total. For example, two skaters pushing off each other swap momentum between them, yet the total momentum of the pair remains constant. External forces would introduce an external impulse and could change the total momentum, but in an isolated collision that external influence is absent, so the total momentum remains constant.