Review session tonight (in NPB 1001, i.e. here):Review session tonight (in NPB 1001, i.e. here): Friday, Sept. 10 th (Woodard), 6:15-8:10pm Subject: chapters.

•Review session tonight (in NPB 1001, i.e. Review session tonight (in NPB 1001, i.e. here): here):

Friday, Sept. 10Friday, Sept. 10thth (Woodard), 6:15- (Woodard), 6:15-8:10pm8:10pm

•Subject: chapters 1-4 Subject: chapters 1-4 (similar to last night)(similar to last night)

•Exam 1 – Mon. Sept. 13*, 8:20-10:20pmExam 1 – Mon. Sept. 13*, 8:20-10:20pm

IMPORTANT NOTICESIMPORTANT NOTICES

Chapter 3 WebAssign homework deadlines Chapter 3 WebAssign homework deadlines are tonight at 11pm (chapter 4 on Sunday, are tonight at 11pm (chapter 4 on Sunday, 11pm).11pm).*Keep an eye on the UF and 2048 course web pages*Keep an eye on the UF and 2048 course web pages

BE PREPARED!BE PREPARED!

Class 8 - Motion in 2D and 3DClass 8 - Motion in 2D and 3DChapter 4 - Friday September 10thChapter 4 - Friday September 10th•Exam instructions

•Brief review of projectile motion

•Uniform circular motion

•Relative motion in two-dimensions

•Example problems

Reading: pages 58 thru 75 (chapter 4) in HRWReading: pages 58 thru 75 (chapter 4) in HRWRead and understand the sample problemsRead and understand the sample problemsAssigned problems from Chapter 4: Assigned problems from Chapter 4: 6, 8, 14, 20, 30, 40, 46, 52, 56, 62 6, 8, 14, 20, 30, 40, 46, 52, 56, 62 (due on Sunday (due on Sunday 12th)12th)

Review of chapter 4 and more problems on MondayReview of chapter 4 and more problems on Monday

Work out solutions in spaces on the examWork out solutions in spaces on the examCircle the correct answersCircle the correct answers

This is a copy of This is a copy of the scantron, the scantron, where you will where you will record your record your answersanswers

1

Name &initials

Full UFID#

Your answersto the test

1

5 digitexamcode

Sectionnumber

•Use a number 2 pencil to fill in the spaces for Use a number 2 pencil to fill in the spaces for answers and for codinganswers and for coding•You can use an eraser but try to avoid doing thisYou can use an eraser but try to avoid doing this

You must sign the back of the scantronYou must sign the back of the scantron

Other important points to note...Other important points to note...

•You are responsible for bringing a self prepared You are responsible for bringing a self prepared formula sheet - formula sheet - hand writtenhand written, 8, 811//22

""x11". Both sides is x11". Both sides is OK.OK.

•Write your section # and UF ID on your formula Write your section # and UF ID on your formula sheet.sheet.

•You must turn in your formula sheet with your You must turn in your formula sheet with your examination sheet at the end of the exam.examination sheet at the end of the exam.

•Bring your ID to the testBring your ID to the test. These will be checked . These will be checked when you enter the exam room.when you enter the exam room.

•As well as coding answers on the pink scantron, you As well as coding answers on the pink scantron, you should also circle answers on the examination sheet.should also circle answers on the examination sheet.

•Do ALL scratch work on the examination sheet in Do ALL scratch work on the examination sheet in the spaces provided.the spaces provided.

0 0 0

0 0

210 0 0 2

0 0

220 0 0

cos 4 21

cos

sin 4 22

sin 4 23

sin 2 4 24

x

y

y

x x v t

v v

y y v t gt

v v gt

v v g y y

A quick reviewA quick review

ˆ ˆ ˆi j kr x y z

2 1ˆ ˆ ˆi j kr r r x y z

ˆ ˆ ˆi j kdr dx dy dz

vdt dt dt dt

ˆ ˆ ˆi j kyx zdvdv dv dv

adt dt dt dt

We will need these equations We will need these equations todaytoday

Acceleration:Acceleration:

Position:Position:

Displacement:Displacement:

Velocity:Velocity:

Uniform circular motionUniform circular motion•Although Although vv does not change, does not change, the direction of the motion does, the direction of the motion does, i.e.i.e. the velocity (a vector) the velocity (a vector) changes.changes.

•Thus, there is an acceleration Thus, there is an acceleration associated with the motion.associated with the motion.

•We call this a centripetal We call this a centripetal acceleration.acceleration.2 2

Acceleration: Period:

1 1Frequency : ; 2

2

v ra T

r vv v

f fT r r

•Since Since vv does not change, the acceleration must be does not change, the acceleration must be perpendicular to the velocity.perpendicular to the velocity.

cos sinˆ ˆi j

p p

p p

x r y r

r x y

Analyzing the motionAnalyzing the motion

2 2t

f t tT

Uniform motion:

Note : 360 2 radianso

cos sinp px r t y r t

sin cos

sin cosˆ ˆi j

x y

x y

x y

v r t v r t

v v t v v t

v v v

Analyzing the motionAnalyzing the motion

cos sinp px r t y r t

p px y

dx dyv v

dt dt

[remember, ]v

v rr

AccelerationAccelerationˆ ˆi j

ˆ ˆ= i j

yx

x y

dvdvdva

dt dt dt

a a

2 2

2 22 2 cos sinx y

v va a a v

r r

sin cos

cos sinx y

x y

v v t v v t

a v t a v t

recall : cos sinp px r t y r t

2 2

cos sinx y

v va t a t

r r

v

r

Relative motionRelative motion

PA PB BAr r r

Position:Position:

PA BA PBPA BA PB R PB

dr dr drv v v v v

dt dt dt

Velocity:Velocity:

PA R PBPA PB

dv dv dva a

dt dt dt

Acceleration (if frame B is “inertial”):Acceleration (if frame B is “inertial”):