1. 1 Lecture #9 of 24 Test advice Review problems Moment of Inertia of disk w/ hole Line Integrals Energy conservation problems Others of interest Energy Pendulum / Simple and solid 2 nd derivative as a spring constant :02

2. 2 Assumed to know Resolving a vector into two components Drawing a free body diagram and using it to setup differential equation of motion Selecting an appropriate coordinate system and reference frame Solving a separable differential equation Applying energy conservation, momentum conservation and understanding basic laws of the trajectory of flying objects Integrating in polar / cylindrical / spherical coords. Doing line integrals :05

3. 3 Best Advice Draw a picture!!! Check that signs and units make sense Check that magnitude of answer makes sense Try limiting conditions :08

4. 4 Richard’s index card (front) :12 Torques and forces on an Extended object operate on its center of mass as if it were a point object.

5. 5 Richard’s Index card (back side) :15  Linear Drag on a sphere (Stokes) Falling from rest w/ gravity  Quadratic Drag on a Sphere (Newton) Falling from rest w/ gravity Decelerating from v without gravity

6. 6 Analogy of 1-D system to roller coaster :20 E1E1 T(x)=E-U(x) <- General 1-D system T(x)=E-mgx <- Roller Coaster E2E2 E3E3 E4E4 x

7. 7 Potential Wells :25 Mass m Spring constant k K > 0 K < 0

8. 8 Taylor Series Expansion :35 Taylor series -- Generic Taylor series -- Potential Can be ignored or set to zero … “gauge invariance” Is already zero for potential evaluated about a critical point x-0

9. 9 L9-1 Potential Wells :35 What is equation of parabola of equivalent curvature?

10. 10 L 9-2 Potential Wells :45 Calculate the Equilibrium separation of two water molecules

11. 11 L8-1 – Area integral of curl :55 Taylor 4.3 (modified) O y x P (1,0) Q (0,1) a c b Calculate, along a,c Calculate, along a,b Calculate, inside a,c Calculate, inside a,b

12. 12 L8-2 Energy problems :65 A block of mass “m” starts from rest and slides down a ramp of height “h” and angle “theta”. a) Calculate velocity “v” at bottom of ramp b) Do the same for a rolling disk (mass “m”, radius r) c) Do part “a” again, in the presence of friction “  ” O y x m h m y x

13. 13 Lecture #9 Wind-up Office hours today 4-6 Wed 4-5:30 Thursday Hand-written index card Official physics league 3’x5’ size :72