2. Linear Momentum and Collisions 9.1 Linear Momentum and Its Conservation9.2 Impulse and Momentum9.3 Collisions9.4 Elastic and Inelastic Collisions in One Dimension9.5 Two-Dimensional Collisions9.6 The Center of Mass9.7 Motion of a System of Particles9.8 (Optional) Rocket Propulsion

3. 9.1 Linear Momentum and Its Conservation The linear momentum of a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity: The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle:

4. Conservation of Momentum for a Two-Particle System Whenever two or more particles in an isolated system interact, the total momentum of the system remains constant.

5. 9.2 Impulse and Momentum The impulse of the force F acting on a particle equals the change in the momentum of the particle caused by that force.

7. EXAMPLE : How Good Are the Bumpers

8. Solution

9. 9.3 Collisions

10. 9.4 Elastic and Inelastic Collisions in One Dimension An elastic collision between two objects is one in which total kinetic energy (as well as total momentum) is the same before and after the collision. An inelastic collision is one in which total kinetic energy is not the same before and after the collision (even though momentum is constant). – perfectly inelastic collision – inelastic collision

11. Elastic Collisions

13. EXAMPLE : A Two-Body Collision with a Spring

14. Solution

15. 9.5 Two-Dimensional Collisions

17. EXAMPLE : Billiard Ball Collision

18. Solution

19. 9.6 The Center of Mass

21. The center of mass of any symmetric object lies on an axis of symmetry and on any plane of symmetry.

23. EXAMPLE : The Center of Mass of Three Particles

24. Solution

25. EXAMPLE : The Center of Mass of a Rod

26. Solution

27. 9.7 Motion of a System of Particles The center of mass of a system of particles of combined mass M moves like an equivalent particle of mass M would move under the influence of the resultant external force on the system.

28. EXAMPLE : The Exploding Rocket

29. Solution

30. Homework.1

31. Homework.2

32. Homework.3

33. Homework.4

34. 9.8 Rocket Propulsion