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Lecture 20: Rotational Dynamics
Week 11 Assignments: (Due 11/03 {Tuesday} by the end of class) Textbook: HW #9 Chp 10: Q4, Q12, P4, P23, P27, P47, P75; Chp 11: P15, P36, P48
MasteringPhysics: - Assignment 9 (Due 11/03 {Tuesday} by the end of class)
Week 11 Reading: Chapter 11.1 – 11.6; 12.1-12.2 -- Giancoli
Today’s Announcements:
- Midterm II is next tuesday
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- 20 questions (~10 MC-TF-SA / 10 Word problems)
* Midterm II is Tuesday 11/03:
- one 3x5” card (both side) of notes
- no problems will directly require calculus, but vectors will be required
- Material to be tested: - Chp 7 --- 7.1-7.2; 7.4 - Chp 8 --- 8.1-8.5 - Chp 9 --- all - Chp 10 --- all - Chp 11 --- TBD
-all clicker Qs; and any examples worked in class
* Midterm class period (11/03) is the last day to turn in late HW# 5 - 8
- no smart devices (even for listening to music)
- arrive early so that seating arrangements can be worked and still provide you most of the time
- If you need OCD accommodations make sure to get them arranged with me (privately) before the exam
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Rolling Motion
2πR
ω = 2π /T
vt = ω R vcm = 2πR/T
vcm = vt (rolling without slipping)
vbottom = -vt + vcm = -ωR + ωR = 0
vt vcm
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Angular Force -- Torque
r
F θ
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Angular Force -- Torque
r
F θ
pivot x
0 < θ < 180 sin θ = (+)
0 > θ > 180 sin θ = (-) F
θ
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Static Equilibrium
Tmax = 103 N θ = 30o
c.of.m(beam) x mb = 75 kg
mp = 50 kg
Lb = 2 m dp = 1.5 m
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- I is called “rotational inertia” or the “moment of inertia”
Rotational Analog of F=ma
r m
at
Ft τ/r = m (α r)
⇒ τ = m r2 α
- the degree to which something resists changing is rotational motion
- what is “rotational mass” ?
τ = I α - rotational analog to F=ma
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Moment of Inertia
rcm dm
Rotation axis
r v
i i i
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Moment of Inertia (Solids – Uniform density)
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Clicker Question:
b) rectangle a) triangle
2) Of the following two shapes, which can be rotated most quickly about the shown rotation axis?
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Clicker Question:
b) rectangle a) triangle
2) Of the following two shapes, which can be rotated most quickly about the shown rotation axis?
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F=40 N La=0.75 m ma=5 kg each
mh=10 kg
rh=0.1 m
mb=30 kg
rb=0.2 m
Beer
What is τ?
What is I?
What is α?
What is ω?