Momentum and Newton's Second Law of Motion
Explains linear momentum, impulse, and the fundamental relationship between net force, mass, and acceleration (F=ma or F=dp/dt).
What is Momentum and Newton's Second Law of Motion?
Product of mass and velocity, p = m v, a vector measured in kg m/s
Key formula / rule: Newton's second law
Key points
- Apply p = mv, F = dp/dt and the impulse-momentum theorem to collisions and sudden forces
Common exam trap
Ignoring the sign reversal of momentum when a body rebounds
Definitions
- Name
Linear momentum
- Definition
Product of mass and velocity, p = m v, a vector measured in kg m/s
- Name
Impulse
- Definition
J = F Δ t, equal to the change in momentum, measured in N s
- Name
Exam insight
- Definition
Catching a ball, airbags and landing on sand all use J = F Δ t: longer contact time means smaller average force
- Name
Worked example
- Definition
0.15 kg ball at 20 m/s rebounding at 20 m/s changes momentum by 6 kg m/s; over 0.01 s the average force is 600 N
Learning objectives
Apply p = mv, F = dp/dt and the impulse-momentum theorem to collisions and sudden forces
Formulae
- Name
Newton's second law
- Expression
Fnet = dp/dt = m a for constant mass
- Name
Impulse-momentum theorem
- Expression
F Δ t = m v - m u
Common mistakes
Ignoring the sign reversal of momentum when a body rebounds
Using F = ma for varying-mass systems such as a rocket
Keywords
momentum
impulse
newton's second law
conservation
collision
force