Announcements

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• Announcements
• Remember -- Tuesday, Oct. 28th, 930 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
• Todays lecture review Chapters 9-14, problem
  solving techniques

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Gravitational forces and energy
m
r
v0
Energy needed to escape Earths gravitational
field, assuming an initial velocity
v0
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Energy needed to go from one stable circular
orbit to another
R1
R2
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Energy needed to go from one stable circular
orbit to another -- Example
How much energy is needed to take a satellite of
mass m100kg from the international space station
(R1RE390 km) to its usual orbit (R2RE600 km)?
R1
R2
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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.

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• 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.).

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Center
of mass
ri
rj
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Position of the center of mass
Velocity of the center of mass
Acceleration of the center of mass
9
Physics of composite systems
Center-of-mass velocity Note that
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A new way to look at Newtons second law
Define linear momentum p mv

• Consequences
• If F 0 ? ? p
  constant
• For system of particles

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Statement of conservation of momentum
If mechanical (kinetic) energy is conserved, then
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Snapshot of a collision
Pi
Impulse
Pf
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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
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r1
v1r1w
w
r2
v2r2w
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 )
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Newtons second law applied to center-of-mass
motion
Newtons second law applied to rotational motion
ri
mi
di
Fi
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Object rotating with constant angular velocity (a
0)
w
R
vRw
v0
Kinetic energy associated with rotation

moment of inertia
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Kinetic energy associated with rolling without
slipping
Distance to axis of rotation
Rolling
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Torque and angular momentum Define angular
momentum For composite object
L Iw
Newtons law for torque
? If ttotal 0 then L constant
In the absence of a net torque on a system,
angular momentum is conserved.
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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
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Notion of equilibrium
Notion of stability
T- mg cos q 0 -mg sin q -maq
Fma ?
r
q
T
tI a ?
r mg sin q mr2 a mraq
Example of stable equilibrium.
mg(-j)
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Analysis of stability
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