Phy 2053 Announcements
Exam 2 is coming soon!!
1.
More Phy 2053 Announcements
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Thursday, April 2, 8:20 – 10:10 pm
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Material from Chapters 5-8 of Serway/Vuille
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Only the sections we covered in class
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20 questions, multiple choice
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There is only one correct answer to the question “In order to receive credit for this
problem, you must correctly code (“bubble in”) your UFID and your 5-digit test
number…”
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Æ I have correctly bubbled my UFID number and 5-digit test code.
Please get there at least 10 minutes early, and preferably 20 minutes
New protocols - stay in your seat until your exam is collected. Raise your
hands; proctors will come to collect it.
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If you want to avoid the long wait at the end, either (a) come early and sit at the
front or (b) finish early
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Please circle your answer on the exam
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Even More Phy 2053 Announcements
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Make-up exam for students missing Exams
1 and 2 will be held Wednesday, April 22
from 7:20 – 9:10 pm
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BRY130: A-ELU
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FLG220: EMM-HER
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FLG230: HEW-LAI
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FLG260: LAM-MON
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FLG270: MOO-P
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LIT121: R-SAW
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MAEB211:SCH-T
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MAT18: U-Z
Very much like the first exam
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Room assignments for Exam 2
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Room to be announced later
You be allowed one handwritten formula sheet
(both sides), 8 ½” x 11” paper
In class review, Tuesday, March 31
Review of Chapter 8
Analogies
linear-----rotation
x becomes θ
m becomes I
v becomes ω
a(T) becomes α
F becomes
If you need to take a make-up because of a
legitimate excuse, please send Prof. Chan and I
an e-mail as soon as possible
HW Assignment 8 due this Wednesday,
March 25
Review: Torque and Angular
Acceleration
τ
Rotational Kinetic Energy
1 2
Iω
2
1
KE = mv 2
2
KE =
Equivalent to
Στ = Iα
∑F =ma
T - mg = ma
− 12 Ma − mg = ma
a=
− mg
M
+m
2
ur
ur
R T = 12 MR 2 α
ur
Rα = a
− R/ T = 12 MR/ a
Conservation of Mechanical Energy
(KEt + KEr + PEg + PEs )i = (KEt + KEr + PEg + PEs )f
Work-Energy Theorem instead of Conservation of
Energy: Wnc = ΔKEt + ΔKER + ΔPE
Look at a as m→0, ∞ or M→0, ∞
1
Example 8.12
Ball rolling down an incline
How fast does it leave the
bottom of the incline?
h
Example: Problem 8-44, p 262
Four objects – a hoop, a solid cylinder, a solid sphere, and
a thin, spherical shell – each have a mass of 4.8 kg and
a radius of 0.23 m. (a) Find the moment of inertia for
each object as it rotates about the axes shown in Table
8.1. (b) Suppose each object rolls down a ramp without
slipping. Rank the translational speed of each object
from highest to lowest. (c) Rank the objects’ rotational
kinetic energy from highest to lowest as the objects roll
down the ramp.
Conservation of Mechanical Energy
(KEt + KE r + PE g + PE s )i = (KEt + KE r + PE g + PE s )f
+ mgh + 0
= mv2/2+Iω2/2 + 0 + 0
I=2mr2/5 and rω=v so Iω2/2= mv2/5
Giving: mgh = mv2/2+ mv2/5 = 7 mv2/10
0
+
0
Note m cancels out as usual
or
θ
v= 10gh/7
Isolated system
Angular Momentum
L=Iω
„
Just like p = mv
Impulse
ΔL
Δt
ur
Δp
Just like ∑ F =
Δt
Στ =
Conservation of Angular Momentum
Στ = 0, Li = Lf or Iiω i = If ω f
Applying Conservation Rules
In an isolated system, the following
three quantities are conserved:
„ Mechanical energy
„ Linear momentum
„ Angular momentum
„
If the net torque is zero, the
angular momentum remains
constant
Conservation of Angular
Momentum states: The angular
momentum of a system is
conserved when the net external
torque acting on the systems is
zero.
Στ = 0, Li = Lf or Iiω i = If ω f
An astrophysical example of angular
momentum conservation
• The Crab Nebula is remnant from the implosion and
subsequent explosion of a massive star in the year 1054
•Located 6300 light years from earth
• The initial angular momentum of the star is conserved
in what remains behind:
• a nebula (a hot gaseous plasma)
• At its center is a ‘neutron star’, more massive than the
sun, but only 10 km in diameter!
• spinning at 30 times per seconds (emitting radio
pulses – ‘pulsar’)
• The really cool part?
•The neutron star rotation is slowing down due to:
• electromagnetic braking
• And Gravitational wave emission?
•Gravitational waves are ripples in space-time
•And from this we can say that the Crab Pulsar is
spherical to better then ~ 1 m
2
Conservation of Angular
Momentum-- Example
How does a skater
spin faster in the
air?
L is conserved
As arms come in-I decreases
ω increases
3