Chapter 9 Momentum and Its Conservation   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 c) FΔt = mΔv F(21) = 2200(-26) F(3.8) = 2200(-26) F(.22) = 2200(-26) 21F = -57200 3.8F = -57200 .22F = -57200 F = -2,723.81 N F = -15,052.63 N F = -260,000 N Do Practice Problems p. 233 # 1-5

ANGULAR MOMENTUM τ = IΔω / Δt τΔt = IΔω   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)