Announcements
• CAPA #11 due this Friday at 10 pm
• Reading: Chapter 9.1-9.4
• Section – this week Lab #4: Rotations
• Midterm Exam #3 on Tuesday November 8th, 2011
 details given on next slides!
 practice exam and solutions on CULearn
 formula sheet and info. posted on web page
• Fraction of all clicker questions answered posted
on CULearn. Email me with your clicker ID, name,
student ID if you believe it is incorrect.
Exam #3 Information
Tuesday, November 8th, 2011
7:30 – 9:15 pm
Location: Same as last two exams (see info page)
The third exam will cover material including Chapters 1-8; CAPA homework
assignments 1-11; Lecture Material through Monday, October 31, and all
Section labs and assignments including the week of October 31-November 4.
Note that the strong emphasis will be on material since that last midterm (i.e.
Chapters 6-8, CAPA 8-11, etc.); however, much of the new material builds upon
the earlier material.
The exam will be 20-25 multiple choice questions. The exam is closed book and
closed notes. Calculators are allowed, but no sharing of calculators. A formula
sheet will be included with your exam, and a preview of that identical sheet is
linked here as a PDF file. There is no need to print and bring this sheet as a copy
will be included with the exam. A practice exam and solutions are available on
the course CULearn page.
CH. 6 Work and Energy
6.1 Work done by a constant force
6.3 Kinetic Energy and Work-Energy Prinl.
6.4 Potential energy
6.5 Conservative and non-conservative forces
6.6. Mechanical energy (M.E.) & its conservation
6.7 Problem solving using conservation of M.E.
6.8 Other forms of energy, energy transformation,
Conservation of Energy (C.E.)
6.9 C.E. with dissipative forces
6.10 Power
CH. 7 Linear Momentum
7.1 Momentum & its relation to force
7.2 Conservation of Momentum (C.M.)
7.3 Collisions & impulse
7.4 Collisions: C.E. & C. M.
7.5 Elastic collisions in 1D
7.6 Inelastic collisions
CH. 8 Rotational Motion
8.1 Angular quantities
8.2 Constant angular acceleration
8.3 Rolling motion
8.4 Torque
8.5 Rotational dynamics (R.D.):
torque and rotational inertia
8.6 Solving problems in R.D.
8.7 Rotational Kinetic Energy
8.8 Conservation of Angular Momentum
Schedule
Today Help Room Hours 1:45 pm – 3:45 pm
Reminder – Dr. Ariel Paul optional review sessions
Wednesdays at 8:00 pm in Duane G125.
Monday in class – exam review clicker questions by
Professor Uzdensky.
No office hours on Monday 2-3 pm.
Clicker Question
Room Frequency BA
A wheel of radius 2 meters is rolling without slipping at a
constant angular velocity of 5 revolutions per minute.
Which is an equivalent expression for w?
A) (1/6) p radians/second
B) (10) p radians/second
C) (1/3) p radians/second
D) (2/3) p radians/second 5rev   1 min    2pradians   p rad / s
E) None of the above
1 min  60 sec   1revolution  6
In two minutes, how far has the wheel traveled (translation)?
A) 0 meters
B) 10 meters
x  vt  wRt  (p / 6)2m(120 s)  40p
C) 5p meters
D) 40p meters
E) None of the above
Conservation of Angular Momentum
Recall:
L = Iω
Angular momentum
Relation to force F = Δp/Δt
τ = ΔL/Δt
Relation to torque
No external force Δp = 0
(momentum is conserved)
ΔL = 0
Momentum
p = mv
No external torque
(angular momentum is conserved)
Li = Lf
Ii ωi = If ωf
Clicker Question
Room Frequency BA
A child stands on the edge of a
merry-go-round.
The child slowly walks towards the
center of the platform.
L  Iw
L
  I 
t
no external torques:
As the child moves toward the
center, the platform’s rotation rate:
A) Increases
B) Decreases
C) Stays the same
L  0 or I iw i  I f w f
Linitial  L final
I iwi  I f w f
 Ii
wf  
If


wi  w
i


Clicker Question
Room Frequency BA
Consider a solid disk of mass M and radius R with
an axis through its center.
An ant of mass m is placed on the rim of the disk.
I
1
MR 2  mR 2
2
The mass-disk system is rotating.
The ant walks toward the center of the disk.
The magnitude of the angular momentum L of
the system:
A) increases B) decreases C) remains constant
Unless an outside
torque is applied,
L = Iω = constant.
As ant moves inward, the kinetic energy of the Because I reduces, ω
system:
increases from the
A) increases B) decreases C) remains constant
ant’s motion.
Clicker Question
Room Frequency BA
A star is rotating with a period of T.
Over a span of a million years, its radius
decreases by a factor of 2.0 due to using up
its nuclear fuel.
What is the new period of the star?
(Recall: Isphere = (2/5) MR2)
A) T/2
B) 2T
C) 4T
Conservation of Angular Momentum:
 Ii
wf  
If


wi


 2

2
MR


5
wi
wf  
 2 M ( R / 2) 2 


D) T/4
L  Iw
L

t
I iw i = I f w f
(if Fext  0)
E) None of these.
w f  4wi
1
T f  Ti
4
Stars shine by converting Hydrogen to Helium (nuclear fusion).
When all the hydrogen is gone, gravity causes the star to
collapse inward (sometimes to a neutron star).
The star radius can change from 1 million miles to 30 miles!
This is a factor of 30,000.
Moment of inertia drops by (3x104)2 ~ 1 billion
Sun rotates around its axis every 24 days.
After a collapse, it would revolve 500 times per second
Pulsar
Bicycle Wheel Demonstration
Static Equilibrium
Static Equilibrium
Static Equilibrium: An object is
(1) not translating (not moving up, down, left, right)
Not translating:
F net  0   i Fi
F  F
x
y
0
(net force is zero)
(each component of the
net force is zero)
(2) not rotating (not spinning CW or CCW).
Not rotating:
 net  0   i  i
(net torque is zero)
Clicker Question
Room Frequency BA
Is the net force on the metal bar zero?
A) Yes
B) No
L
Is the the metal in static equilibrium?
A) Yes
B) No
Consider rotations about the middle of the bar.
 net 

i
  F ( L / 2)  F ( L / 2)   FL  0
i
Net positive torque will cause the bar to rotate (CCW).
Fnet = 0 but the bar will rotate anyway.