Impulse and Momentum
Summary
- Momentum…
- is a quantity that describes an object's resistance to stopping (a kind of "moving inertia").
- is represented by the symbol p (boldface).
- is the product of an object's mass and velocity.
p = mv
- is a vector quantity (since velocity is a vector and mass is a scalar).
- Impulse…
- is a quantity that describes the effect of a net force acting on an object (a kind of "moving force").
- is represented by the symbol J (boldface).
- is the product of the average net force acting on an object and its duration.
J = F∆t
- is the force-time integral.
J = ⌠
⌡F dt - is a vector quantity (since force is a vector and time is a scalar).
- Impulse-Momentum Theorem
- The impulse-momentum theorem states that the change in momentum of an object equals the impulse applied to it.
J = ∆p
- If mass is constant, then…
F∆t = m∆v
- If mass is changing, then…
F dt = m dv + v dm
- The impulse-momentum theorem is logically equivalent to Newton's second law of motion (the force law).
- The impulse-momentum theorem states that the change in momentum of an object equals the impulse applied to it.
- Units
- The SI unit of impulse is the newton second.
- The SI unit of momentum is the kilogram meter per second.
- These units of impulse and momentum are equivalent.
[N s = kg m/s]
I | II | |
---|---|---|
1st law | inertia m |
momentum p = mv |
2nd law | force law F = ma |
impulse-momentum theorem J = ∆p |
3rd law | action-reaction +F1 = −F2 |
conservation of momentum ∑p = ∑p0 |
- Specific impulse
- is a measure of the efficacy of rocket propellants.
- if defined as impulse per mass (or thrust per mass flow rate)
- is equal to exhaust velocity and has the SI unit of meter per second.
Jsp[m/s] = J = T = v m qm - if defined as impulse per weight (or thrust per weight flow rate)
- is equal to exhaust velocity divided by acceleration due to gravity and has the SI unit of second.
Jsp[s] = J = T = v mg qmg g