1. Today’s lecture – review Chapters 9-14, problem solving techniques
Announcements
Remember -- Tuesday, Oct. 28th, 9:30 AM – Second exam (covering Chapters 9-14 of HRW) – Bring the following:
1 equation sheet
Calculator
Pencil
Clear head
Note: If you have kept up with your HW, you may drop your lowest exam grade
Today --Thursday, Oct. 23th, 4 PM – Physics Colloquium by Professor Bernd Schüttler, Dept. of Physics, U. Ga – will discuss the analysis of biological systems in terms of a physical and mathematical model
Today’s lecture – review Chapters 9-14, problem solving techniques
12/7/2018
PHY Lecture 14R

2. Gravitational forces and energym r v0
Energy needed to escape Earth’s gravitational field, assuming an initial velocity : v0
12/7/2018
PHY Lecture 14R

3. Energy needed to go from one stable circular orbit to another:
12/7/2018
PHY Lecture 14R

4. Energy needed to go from one stable circular orbit to another --
Example:
How much energy is needed to take a satellite of mass m=100kg from the international space station (R1=RE+390 km) to its usual orbit (R2=RE+600 km)? R1 R2
12/7/2018
PHY Lecture 14R

5. Problem solving skills
Equation Sheet
Math skills
Advice:
Keep basic concepts and equations at the top of your head.
Practice problem solving and math skills
Develop an equation sheet that you can consult.
12/7/2018
PHY Lecture 14R

6. Visualize problem – labeling variables
Problem solving steps
Visualize problem – labeling variables
Determine which basic physical principle applies
Write down the appropriate equations using the variables defined in step 1.
Check whether you have the correct amount of information to solve the problem (same number of knowns and unknowns.
Solve the equations.
Check whether your answer makes sense (units, order of magnitude, etc.).
12/7/2018
PHY Lecture 14R

7. Center
of mass ri rj
12/7/2018
PHY Lecture 14R

8. Position of the center of mass:
Velocity of the center of mass:
Acceleration of the center of mass:
12/7/2018
PHY Lecture 14R

9. Physics of composite systems:
Center-of-mass velocity:
Note that:
12/7/2018
PHY Lecture 14R

10. A new way to look at Newton’s second law:
Define linear momentum p = mv
Consequences:
If F =   p = constant
For system of particles:
12/7/2018
PHY Lecture 14R

11. Statement of conservation of momentum:
If mechanical (kinetic) energy is conserved, then:
12/7/2018
PHY Lecture 14R

12. Snapshot of a collision:Pi
Impulse: Pf
12/7/2018
PHY Lecture 14R

13. angular “displacement”  q(t) angular “velocity” 
Angular motion
angular “displacement”  q(t)
angular “velocity” 
angular “acceleration”  s
“natural” unit == 1 radian
Relation to linear variables: sq = r (qf-qi)
vq = r w
aq = r a
12/7/2018
PHY Lecture 14R

14. Special case of constant angular acceleration: a = a0:
v1=r1w w r2
v2=r2w
Special case of constant angular acceleration: a = a0:
w(t) = wi + a0 t
q(t) = qi + wi t + ½ a0 t2
( w(t))2 = wi2 + 2 a0 (q(t) - qi )
12/7/2018
PHY Lecture 14R

15. Newton’s second law applied to center-of-mass motion
Newton’s second law applied to rotational motion ri mi di Fi
12/7/2018
PHY Lecture 14R

16. Object rotating with constant angular velocity (a = 0)
v=Rw
v=0
Kinetic energy associated with rotation:
“moment of inertia”
12/7/2018
PHY Lecture 14R

17. Kinetic energy associated with rolling without slipping:
Distance to axis of rotation
Rolling:
12/7/2018
PHY Lecture 14R

18. Torque and angular momentum Define angular momentum:
For composite object: L = Iw
Newton’s law for torque:
 If ttotal = 0 then L = constant
In the absence of a net torque on a system,
angular momentum is conserved.
12/7/2018
PHY Lecture 14R

19. Center-of-mass
Torque on an extended object due to gravity (near surface of the earth) is the same as the torque on a point mass M located at the center of mass. mi ri
rCM
12/7/2018
PHY Lecture 14R

20. Notion of equilibrium:
Notion of stability:
T- mg cos q = 0
-mg sin q = -maq
F=ma  r q T
t=I a 
r mg sin q = mr2 a = mraq
Example of stable equilibrium.
mg(-j)
12/7/2018
PHY Lecture 14R

21. Analysis of stability:
12/7/2018
PHY Lecture 14R

22. 12/7/2018
PHY Lecture 14R

23. 12/7/2018
PHY Lecture 14R

24. 12/7/2018
PHY Lecture 14R

25. 12/7/2018
PHY Lecture 14R

26. 12/7/2018
PHY Lecture 14R