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In this chapter you will:
 Describe momentum and impulse and apply them
to the interactions between objects.
Relate Newton’s third law of motion to conservation
of momentum.
Explore the momentum of rotating objects.
Chapter 9 Sections
 Section 9.1: Impulse and Momentum
 Section 9.2: Conservation of
Momentum
Section 9.1 Impulse and
Momentum
 Objectives
 Define the momentum of an object.
 Determine the impulse given to an
object.
 Define the angular momentum of an
object.
IMPULSE AND MOMENTUM
 I suggest you read chapter 9 from the old book.
 F = ma
 a = Δv / Δt
 F = m(Δv / Δt)
 Multiply both sides by Δt
FΔt = mΔv
IMPULSE AND MOMENTUM
 Impulse – is the product of force and time interval over which it
acts. It is a vector quantity in the direction of the force. It is
measured in units Newton seconds (N*s). If force varies with time it
is found by determining the Area under the curve of a Force Time
Graph as in Figure 9-1.
 Momentum - product of an object’s mass and velocity. It is a vector
quantity that has the same direction as the velocity of the object. It
is denoted by “p” (lower case). It is mass in motion. The unit for
Momentum is kg m/s. To find Momentum you use
p = m*v
Δp = mΔv
 FΔt = mΔv = mvF – mvI = Δp = pF – pI
 1 N*s = 1 kg*m/s
IMPULSE AND MOMENTUM
 Impulse Momentum Theorem – states impulse given to
an object is equal to its change in momentum. Or the
impulse of an object is equal to the object’s Final
Momentum Minus its Initial Momentum.
Thus Ft = p or FΔt = pF – pI
 If the force is constant the Impulse is the Product of the
Force multiplied by the time interval over which it acts.
 If Force is not constant then the Impulse is found
using the Average Force multiplied by the time
interval or by finding the area under the curve of a
Force Time Graph.
USING THE IMPULSE MOMENTUM
THEOREM TO SAVE LIVES
 Go over baseball example p. 231
 A large impulse results from a large force over a short
period of time or a small force over a long period of
time.
 An airbag reduces the force by increasing the time
interval during which it acts.
USING THE IMPULSE MOMENTUM
THEOREM TO SAVE LIVES
 Example Problem 1 p. 232
 a) FΔt = mΔv



b) FΔt = mΔv
F(21) = 2200(-26) F(3.8) = 2200(-26)
21F = -57200
3.8F = -57200
F = -2,723.81 N
F = -15,052.63 N
 Do Practice Problems p. 233 # 1-5
c) FΔt = mΔv
F(.22) = 2200(-26)
.22F = -57200
F = -260,000 N
ANGULAR MOMENTUM
 τ = IΔω / Δt
 τΔt = IΔω
 Angular Impulse – is the product of the Torque and the time interval. It equals
τΔt.
 Angular Momentum – is the product of the Moment of Inertia and the Angular
Velocity. It equals IΔω. It is denoted by “L”.
 Angular Impulse Angular Momentum Theorem – states the angular impulse on
an object is equal to the object’s final angular momentum minus the object’s initial
angular momentum.
 If there are no torques acting on an object then its angular momentum is constant.
 Do 9.1 Section Review p. 235 # 6-9 (Skip 10-12)