- Momentum is a conserved quantity.
- The total momentum of a closed system is constant.
- When objects interact, their total momentum before the interaction is the same as after the interaction.
∑pbefore = ∑pafter
- There are several conventions for writing before and after in mathematical shorthand.
∑p = ∑p′ = ∑p″ = ∑p‴ primes for after ∑p0 = ∑p nought for before Σq = ∑p q for before ∑pi = ∑pf initial and final
- Numbered subscripts are usually used to identify individual objects.
p1 + p2 + p3 + … = p1′ + p2′ + p3′ + … m1v1 + m2v2 + m3v3 + … = m1v1′ + m2v2′ + m3v3′ + …
- The law of conservation of momentum is logically equivalent to Newton's third law of motion (the action-reaction law).
I II 1st law inertia
p = mv
2nd law force law
F = ma
J = Δp
3rd law action-reaction
+F1 = −F2
conservation of momentum
∑p = ∑p0
Related concepts of dynamics
- Momentum is a vector quantity, so you need to pay attention to direction.
- Momentums pointing in a convenient direction should be positive.
- Momentums pointing in the opposite direction must be negative.
- Momentums pointing in arbitrary directions are dealt with in another section of this book.
- Recoil occurs when one object moves abruptly backward in reaction to pushing or propelling another object forward.
- The two objects are initially in contact with one another and are therefor at rest relative to one another (∑p = 0).
- Momentum is conserved, so the total momentum afterwards is still zero (∑p′ = 0).
- In order for the total momentum to remain zero, the momentum of one object is equal and opposite the other (+p1′ = −p2′).
- Momentum is conserved for all types of collisions.
- Two objects collide and separate
p1 + p2 = p1′ + p2′ m1v1 + m2v2 = m1v1′ + m2v2′
- Two objects collide and stick together
p1 + p2 = p1+2′ m1v1 + m2v2 = (m1 + m2)v′