The Physics
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Opus in profectus

# 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 = Ft

• 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…

Ft = mv

• 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]

Related concepts of dynamics
III
1st lawinertia
m
momentum
p = mv
2nd lawforce law
F = ma
impulse-momentum theorem
J = ∆p
3rd lawaction-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