45-CA_Lesson_1_Impulse_and_Momentum.pptx

impulse

1. Impulse and Momentum Lesson 1

2. Objectives: Identify the impulse and its physical meaning Analyze the relationship between the impulse and the momentum

3. New Vocabulary impulse momentum impulse-momentum theorem angular momentum angular impulse–angular momentum theorem

4. CTQ How do air bags work to save lives?

5. Review Vocabulary angular velocity: the angular displacement of an object divided by the time needed to make the angular displacement.

6. Search activity What is the impulse? What is the mathematical formula of impulse?

7. Discussion According to the impulse definition, what is the SI unit of the impulse?

8. Let’s remember What is the vector quantity? What is the scalar quantity? Give an example about each one of them.

9. Let’s make search What is the momentum? What is the mathematical formula for momentum? What is the SI unit of the momentum?

10. Impulse-Momentum Theorem The impulse on an object is the product of the average force on the object and the time interval during which it acts. Impulse is measured in newton-seconds. The product of the object’s mass and the object’s velocity is the momentum of the object. Momentum p = m v Momentum is a vector quantity. Momentum is measured in kg ·m/s.

11. Impulse-Momentum Theorem The impulse-momentum theorem states that the impulse on an object is equal to the change in its momentum. Impulse-Momentum Theorem F Δ t = p f − p i

12. Impulse-Momentum Theorem Use with Example Problem 1. Problem Assume that there is a passenger of 85-kg mass in the vehicle described in Example Problem 1. For both gentle and hard braking situations, calculate the impulse and average force needed to bring the person to a stop along with the vehicle. Response SKETCH AND ANALYZE THE PROBLEM Sketch the situation. Indicate the initial and final momentum and the impulse. List the knowns and unknowns. KNOWN UNKNOWN v i = +26 m/s Δ t gentle = 21 s F Δ t = ? v f = 0 m/s Δ t hard = 3.8 s F gentle = ? m p = 85 kg F hard = ? SOLVE FOR THE UNKNOWN Determine the initial and final momentum of the person. Use the impulse-momentum theorem to determine the impulse and force. m p = 85 kg v i = 26 m/s p i p f ● impulse

13. KNOWN UNKNOWN v i = +26 m/s Δ t gentle = 21 s F Δ t = ? v f = 0 m/s Δ t hard = 3.8 s F gentle = ? m p = 85 kg F hard = ? Impulse-Momentum Theorem EVALUATE THE ANSWER Impulse is measured in kg · m/s and f orce is measured in newtons, so the units are correct. The force needed to stop a person is much less than that needed to stop the car. Use with Example Problem 1. Problem Assume that there is a passenger of 85-kg mass in the vehicle described in Example Problem 1. For both gentle and hard braking situations, calculate the impulse and average force needed to bring the person to a stop along with the vehicle. Response SKETCH AND ANALYZE THE PROBLEM Sketch the situation. Indicate the initial and final momentum and the impulse. List the knowns and unknowns. SOLVE FOR THE UNKNOWN Determine the force for the cases of gentle and emergency braking. m p = 85 kg v i = 26 m/s p i p f ● impulse − 2.2×10 3 kg · m/s

14. Angular Momentum Newton’s second law for rotational motion ( τ = I   Δ ω /Δ t ) states that angular velocity of a rotating object changes only if torque is applied to it. This equation can be rearranged in the same way as Newton’s second law of motion was, to produce τ Δ t = I   Δ ω . The left side of this equation is the angular impulse of the rotating object and the right side can be rewritten as Δ ω = ω f − ω i .

15. Angular Momentum The angular momentum of an object is equal to the product of a rotating object’s moment of inertia and angular velocity. Angular Momentum L = I   Δ ω Angular momentum is measured in kg·m 2 /s.

16. Angular Momentum Just as the linear momentum of an object changes when an impulse acts on it, the angular momentum of an object changes when an angular impulse acts on it. Thus, the angular impulse on the object is equal to the change in the object’s angular momentum, which is called the angular impulse-angular momentum theorem. Angular Impulse-Angular Momentum Theorem τ Δ t = L f − L i

17. Angular Momentum If there are no forces acting on an object, its linear momentum is constant. If there are no torques acting on an object, its angular momentum is constant. Because an object’s mass cannot be changed, if its momentum is constant, then its velocity is also constant.

18. Angular Momentum The angular velocity of an object can change, however, even if no torques are acting on it. This is because the moment of inertia depends on the object’s mass and the way it is distributed about the axis of rotation. For example, a diver can control her angular velocity by changing her moment of inertia.

19. Angular Momentum EVALUATE THE ANSWER The units are correct: Angular momentum is measured in kg · m 2 /s. Use with Example Problem 2. Problem A DVD ( I = 2.7×10 −5 kg · m 2 ) rotates at 25.5 rotations per second when the inner edge is being read and at 10.5 rotations per second when the outer edge is being read. What is the change in angular momentum as the disc is read from the inner edge to the outer edge? Response SKETCH AND ANALYZE THE PROBLEM List the knowns and unknowns. KNOWN UNKNOWN I = 2.7×10 −5 kg · m 2 Δ L = ? ω i = 25.5 rotations/s ω f = 10.5 rotations/s SOLVE FOR THE UNKNOWN Determine the initial and final angular momentums. Then find the difference.

20. Quiz kg/s D kg  m/s C kg  m/s 2 B m/s 2 A Which are the units for momentum? 1. CORRECT

21. Quiz a 75-kg person sitting still D a 5-kg ball moving at 40 m/s C a 25-kg wagon moving at 5 m/s B a 10-kg dog running at 15 m/s A Which has the greatest momentum? 2. CORRECT

22. Quiz angular momentum D momentum C angular impulse B impulse A Which is the product of a rotating object’s moment of inertia and angular velocity? 3. CORRECT

23. Quiz angular momentum D impulse C angular impulse–angular momentum theorem B impulse-momentum theorem A Which is represented by the following equation? F Δ t = p f − p i 4. CORRECT

24. Quiz angular impulse-angular momentum theorem D impulse C impulse-momentum theorem B angular momentum A Which is represented by the following equation? L = Iω 5. CORRECT