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).
• 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]

• 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