Announcements

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 InformationTuesday, 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 Energy6.1 Work done by a constant force6.3 Kinetic Energy and Work-Energy Prinl.6.4 Potential energy6.5 Conservative and non-conservative forces6.6. Mechanical energy (M.E.) & its conservation6.7 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 forces6.10 Power

CH. 7 Linear Momentum7.1 Momentum & its relation to force7.2 Conservation of Momentum (C.M.)7.3 Collisions & impulse7.4 Collisions: C.E. & C. M.7.5 Elastic collisions in 1D7.6 Inelastic collisions

CH. 8 Rotational Motion8.1 Angular quantities8.2 Constant angular acceleration8.3 Rolling motion8.4 Torque8.5 Rotational dynamics (R.D.):

torque and rotational inertia8.6 Solving problems in R.D.8.7 Rotational Kinetic Energy8.8 Conservation of Angular Momentum

ScheduleToday 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.

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/secondB) (10) p radians/secondC) (1/3) p radians/secondD) (2/3) p radians/secondE) None of the above

Clicker Question Room Frequency BA

In two minutes, how far has the wheel traveled (translation)?A) 0 metersB) 10 metersC) 5p metersD) 40p metersE) None of the above

min1

5rev sradrevolution

radians/

61

2

sec60

min1

40)120(2)6/( smRtvtx

Recall:

Momentum p = mv L = Iω Angular momentum

Relation to force F = Δp/Δt τ = ΔL/Δt Relation to torque

No external force Δp = 0 ΔL = 0 No external torque (momentum is conserved) (angular momentum is conserved)

Ii ωi = If ωf

Conservation of Angular Momentum

Li = Lf

L I

I Lt

no external torques:

L 0 or Ii i I f f

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.

As the child moves toward the center, the platform’s rotation rate:

A) IncreasesB) DecreasesC) Stays the same

finalinitial LL

ffii II

if

if I

I

i

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.

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

As ant moves inward, the kinetic energy of the system:

A) increases B) decreases C) remains constant

Unless an outside torque is applied,L = Iω = constant.

Because I reduces, ω increases from the

ant’s motion.

I 1

2MR2 mR2

Clicker Question Room Frequency BA

L I

Lt

Ii i = I f f

(if Fext 0)

Conservation of Angular Momentum:

A) T/2 B) 2T C) 4T D) T/4 E) None of these.

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)

Clicker Question Room Frequency BA

if

if I

I

if

RM

MR

2

2

)2/(5

25

2

if 4

if TT4

1

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

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!

Pulsar

Bicycle Wheel Demonstration

Static Equilibrium

Static Equilibrium: An object is

(1) not translating (not moving up, down, left, right)

(2) not rotating (not spinning CW or CCW).

Not translating:

Fnet 0 Fi

i

Fx Fy 0

(net force is zero)

(each component of the net force is zero)

Static Equilibrium

net 0 ii (net torque is zero)Not rotating:

Is the net force on the metal bar zero?A) Yes B) No

Consider rotations about the middle of the bar.

Clicker Question Room Frequency BA

Is the the metal in static equilibrium?A) Yes B) No

i

inet

Fnet = 0 but the bar will rotate anyway.

L

FLLFLF )2/()2/( 0

Net positive torque will cause the bar to rotate (CCW).