Section 9.2 Conservation of Momentum  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) -875 since gas shoots -84vAF = -30.625 backwards sending vAF = .365 m/s Astronaut forward Do Practice Problems p. 240 # 19-21

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