Objectives
Relate Newton’s third law to conservation
of momentum.
Recognize the conditions under which
momentum is conserved.
Solve conservation of momentum
problems.
TWO PARTICLE COLLISIONS
 I suggest you read chapter 9 from the old book.
 The forces that 2 objects exert on each other are equal but opposite in direction
according to Newton’s 3rd Law.
 So with figure 9-6
FDonC = -FConD
 That leads to
 pCF – pCI = -(pDF – pDI)
 Or pCF + pDF = pCI + pDI
 This tells us that the sum of the momenta of the balls is the same before and
after the collision.
 Conserved Properties – properties that are the same before and after an
interaction. Examples are energy and momentum.
MOMENTUM IN A CLOSED,
ISOLATED SYSTEM
 Closed System – a system that does not gain or lose mass.
 Isolated System – a closed system on which the net external
force is zero.
 Closed Isolated System – collection of objects such that
neither matter nor energy can enter or leave the collection.
 Law of Conservation of Momentum – states that the
momentum of any closed isolated system does not change.
 pAI + pBI = pAF + pBF
 mAvAI + mBvBI = mAvAF + mBvBF
MOMENTUM IN A CLOSED,
ISOLATED SYSTEM
 Example Problem 2 p. 237
 mAvAI + mBvBI = mAvAF + mBvBF
 1875(23) + 1025(17) = 1875vF + 1025vF
 43125 + 17425 = 2900vF
 60550 = 2900vF
 20.88 m/s = vF

 Do Practice Problems p. 238 # 13-18
RECOIL
 The momenta of the skaters after the push are equal
and opposite in direction.
PROPULSION IN SPACE
 Example Problem 3 p. 240
 mAvAI + mBvBI = mAvAF + mBvBF
 84(0) + .035(0) = 84vAF + .035(-875)
 -84vAF = -30.625
 vAF = .365 m/s
 Do Practice Problems p. 240 # 19-21
-875 since gas shoots
backwards sending
Astronaut forward
TWO DIMENSIONAL COLLISIONS
 Skip Example 4
 Skip Practice Problems p. 243 # 22-25
CONSERVATION OF ANGULAR
MOMENTUM
 Angular Impulse – the product of the torque and the time interval.
 Angular Momentum – product of the moment of inertia and the
angular velocity.
 Angular Impulse Angular Momentum Theorem – states that the
angular impulse is equal to the object’s change in angular momentum.
 The Law of Conservation of Angular Momentum – states that if no
net external Torque acts on an object, then its angular momentum does
not change. An object’s initial angular momentum is equal to its final
angular momentum.
L1 = L2
 Don’t worry about these formulas to much.
LI = LF
IIωI = IFωF
ωF / ωI = II / IF
f = ω / 2Π
fF / fI = II / IF
TOPS AND GYROSCOPES
 Because of the conservation of angular
momentum, the direction of rotation of a
spinning object can be changed only by
applying a torque.
 SKIP 9.2 Section Review p. 245 # 26-31