Chapter 10: Systems of Particles
Momentum

Newton’s laws can be expressed very neatly in terms of momentum, a vector
quantity of great important in physics. The momentum of a single particle is defined
as the product of the mass and the velocity of the particle (p = mv)

The momentum has the same direction as the velocity vector

Newton’s First Law states that in absence of external forces, the velocity of a
particle remains constant. Therefore, the first law therefore states that the
momentum remains constant

To express the Second Law in terms of momentum, we note that since the mass is
constant, the time derivative is
o
dp/dt = m * dv/dt
o
dp/dt = ma
o
dp/dt = F

We can also express Newton’s Third Law in terms of momentum. Whenever two
bodies exert forces on each other, the resulting changes of momentum are of equal
magnitudes and of opposite directions
o
P = p1 + p2 + p3 + …
+pN

The rates of change of p1 and p2 are exactly opposite (if they are the only 2 particles
in a closed system)
o
Dp1/dt =  dp2/dt

Momentum is conserved, but kinetic energy is not conserved
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 Spring '08
 Kolomeisky
 Physics, Center Of Mass, Kinetic Energy, Mass, Momentum, internal forces

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