Mr. Borosky Physics Section 9.2 Notes Page 3 of 3

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.

I suggest you read chapter 9 from the old book.

Read intro paragraph p. 236

TWO PARTICLE COLLISIONS

Read Section.

The forces 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)

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

Read Section.

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

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

Read Section.

The momenta of the skaters after the push are equal and opposite in direction.

PROPULSION IN SPACE

Read Section.

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

Read Section.

Skip Example 4

Skip Practice Problems p. 243 # 22-25

CONSERVATION OF ANGULAR MOMENTUM

Read Section.

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

Read Section.

Because of the conservation of angular momentum, the direction of rotation of a spinning object can be changed only by applying a torque.

Do 9.2 Section Review p. 245 # 26-31