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

- 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

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

Angular Force -- Torque

r

F θ

Angular Force -- Torque

r

F θ

pivot x

0 < θ < 180 sin θ = (+)

0 > θ > 180 sin θ = (-) F

θ

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

- 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

Moment of Inertia

rcm dm

Rotation axis

r v

i i i

Moment of Inertia (Solids – Uniform density)

Clicker Question:

b) rectangle a) triangle

2) Of the following two shapes, which can be rotated most quickly about the shown rotation axis?

Clicker Question:

b) rectangle a) triangle

2) Of the following two shapes, which can be rotated most quickly about the shown rotation axis?

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?