2. Chapter 9 Linear Momentum Classical Mechanics beyond the Newtonian Formulation

3. Introduction – Our approach Introducing momentum and impulse Conservation of momentum Conservation of energy and/or momentum in collisions Center of mass and Newton’s Second Law Problem solving Comparing energy and momentum Capstone project (introduce now)

4. Momentum and Impulse Definition of momentum of a simple object Newton’s Second Law expressed in terms of momentum (simple objects at first) Impulse and the Impulse – Momentum Principle (or Relation or Theorem) Examples (inc, egg toss, martial arts, Slylock Fox) Demo: Super ball vs Clay ball impulse Lab preparation assignment

5. Conservation of Momentum Momentum of a system defined Impulse on a system defined Same Impulse-Momentum principle? Condition for Conservation of Momentum Statement of Conservation of Momentum Underlying symmetry of nature Examples from the class?

6. Conservation of Momentum… Examples (planned) –Train car/gravel/bridge –Catch in ice boat –Astronaut catch in space –Why do rockets work in space? –Recoil –LA Warehouse driver grievance/accident –Other problems?

7. Conservation of Energy & Momentum in Collisions Elastic and Inelastic Collisions Examples/Discussion Elastic Collisions in 1-D Inelastic Collisions (perfectly, partially) Collisions in 2,3-D Concerns/Questions?

8. Center of Mass and Translational Motion Center of Mass –Definition of Center of Mass (CM) –Finding the CM experimentally Expressing Newton’s Second Law for a System –So that’s the “point” of translational motion! Examples

9. Problem-Solving Putting all the frameworks together (see)see –What to look for? From the Capstone project What’s new in J = Δp –Diagrams of before & after m’s, vectors v i, v f –and J or F av and Δt, or F(t) and t i and t f. And for Δp = 0, just the former And for both: Momentum Ledger (see)see J = Δp chart (see)see Δp = 0 chart (see)see

10. Energy & Momentum Three ways they are similar Three ways they are different Examples of their difference Energy & Momentum misconceptions in practice – a short play

11. the end

12. Momentum inventory ledger ∑ p∑ J Eqn.x-comp.y-comp.z-compx-comp.y-comp.z-comp (1) Before (i) (2) After (f) (2)-(1) ∆p = Momentum Impulse Principle ∆p x = J x ∆p y = J y ∆p z = J z Conservation of Momentum (when J = 0) ∆p x = 0∆p y = 0∆p z = 0 back

13. Using Impulse-Momentum Principle The Physical situation Choose/identify systems, objects, forces Choose coords., Sketch relevant F, ∆t, p i, p f Momentum Inventory Ledger Implement Impulse-Momentum Prin. Mathematical representation Solution Problem back

14. Using Conservation of Momentum The Physical situation Choose/identify systems, objects, forces Choose coordinates; Sketch p i, p f vectors Momentum Inventory Ledger Implement Cons. of Momentum Mathematical representation Solution Problem back