Physics 218, Lecture XIX 1

Physics 218Lecture 19

Dr. David Toback

Physics 218, Lecture XIX 2

Checklist for Today• Things due Last Thursday:

– Read Chapters 12 & 13• Things that were due Monday:

– Chapter 10 & 11 HW on WebCT• Things that are due tomorrow for

Recitation– Chapter 12&13 problems– Read Lab hand out on webpage

• Things due next Monday– Chapter 12 & 13 in WebCT

Physics 218, Lecture XIX 3

The ScheduleThis Week (3/31) • Mon: Chapter 10 & 11 due material in WebCT• Tues: Second lecture on Chaps 12 & 13• Wed: Recitation on Chapters 12 & 13, Lab• Reading for Thurs: Chapters 14-16• Thurs Lecture: Chap 14 Next week (4/7)• Mon: Chapter 12 & 13 material due in WebCT• Tues: Second Lecture on Chap 14• Wed: Recitation on Chap 14, Lab• Thurs Lecture: Chap 15, Part 1Week after that (4/14)• Monday: Chapter 14 due in WebCT• Tues: Exam 3 (Chaps 10-13)• Wed: Recitation on Chap 15, Lab• Thurs: Lecture on Chap 15, Part 2

Physics 218, Lecture XIX 4

Overview• Chapters 12-16 are about

Rotational Motion• While we’ll do Exam 3 on Chapters

10-13, we’ll do the lectures on 12-16 in six combined lectures

• Give extra time after the lectures to Study for the exam

• The book does the math, I’ll focus on the understanding and making the issues more intuitive

Physics 218, Lecture XIX 5

Physics 218, Lecture XIX 6

Overview: Rotational Motion

• Take our results from “linear” physics and do the same for “angular” physics

• Analogue of –Position ←–Velocity ←–Acceleration ←–Force–Mass–Momentum–Energy

Start here!

Ch

ap

ters

1-3

Physics 218, Lecture XIX 7

Rotation and Translation

Objects can both translate and rotate at the same time. They do both around their center of mass.

Physics 218, Lecture XIX 8

Rolling without Slipping

•In reality, car tires both rotate and translate

•They are a good example of something which rolls (translates, moves forward, rotates) without slipping

•Is there friction? What kind?

Physics 218, Lecture XIX 9

Derivation

The trick is to pick think of the wheel as sitting still and the ground moving past it with speed V.

Velocity of ground (in bike frame) = -R

Velocity of bike (in ground frame) = R

Physics 218, Lecture XIX 10

Bicycle comes to RestA bicycle with initial linear velocity V0

(at t0=0) decelerates uniformly (without slipping) to rest over a distance d. For a wheel of radius R:

a)What is the angular velocity at t0=0?b)Total revolutions before it stops?c)Total angular distance traversed

by the wheel?d)The angular acceleration?e)The total time until it stops?

Physics 218, Lecture XIX 11

Uniform Circular Motion

• Fancy words for moving in a circle with constant speed

• We see this around us all the time– Moon around the earth– Earth around the sun– Merry-go-rounds

• Constant and Constant R

Physics 218, Lecture XIX 12

Uniform Circular Motion - Velocity

•Velocity vector = |V| tangent to the circle

•Is this ball accelerating?

–Yes! why?

Physics 218, Lecture XIX 13

Centripetal Acceleration

• “Center Seeking”

• Acceleration vector= V2/R towards the center

• Acceleration is perpendicular to the velocity

)r̂(Rv

a2

R

direction r̂

Physics 218, Lecture XIX 14

Circular Motion: Get the speed!

Speed = distance/time Distance in 1 revolution

divided by the time it takes to go around once

Speed = 2r/TNote: The time to go around once is known as the Period, or T

Physics 218, Lecture XIX 15

The Trick To Solving Problems

)r̂(Rv

m

amF2

Physics 218, Lecture XIX 16

Banking Angle

You are a driver on the NASCAR circuit. Your car has mass m and is traveling with a speed V around a curve with Radius R

What angle, , should the road be banked so that no friction is required?

Physics 218, Lecture XIX 17

Skidding on a CurveA car of mass m rounds a curve on a flat road of radius R at a speed V. What coefficient of friction is required so there is no skidding?Kinetic or static friction?

Physics 218, Lecture XIX 18

Conical PendulumA small ball of

mass m is suspended by a cord of length L and revolves in a circle with a radius given by

r = Lsin.

1.What is the velocity of the ball?

2.Calculate the period of the ball

Physics 218, Lecture XIX 19

Exam 2

• Class average for the 2nd exam (including the 5 points) was 65%– Average for first two exams is a 69%

• Note for students who didn’t take the mini-practice exam:

•Exam 2 Average=51%!!! High score=75

•Two exam average = 60%, almost 20 points below those who took it

• Planning on only a small curve for now, will decide after the 3rd exam

Physics 218, Lecture XIX 20

Should you Q-drop?

•Many have asked “should I q-drop?” –Talk to your advisor and read my FAQ!

–Generic advice: Drop if you can’t keep up with the homework by yourself

Physics 218, Lecture XIX 21

Next Time

•Wednesday Recitation: Recitation on Chapters 12 & 13

•Wednesday Lab: Elastic Collisions

•Thursday: Lecture on Chapter 14

•Monday: Chapters 12 & 13 due in WebCT

Physics 218, Lecture XIX 22

Physics 218, Lecture XIX 23

Circular Motion Example

A ball of mass m is at the end of a string and is revolving uniformly in a horizontal circle (ignore gravity) of radius R. The ball makes N revolutions in a time t.

a)What is the centripetal acceleration?

b)What is the centripetal force?

Physics 218, Lecture XIX 24

Ball on a String

A ball at the end of a string is revolving uniformly in a horizontal circle (ignore gravity) of radius R. The ball makes N revolutions in a time t.

What is the centripetal acceleration?

Physics 218, Lecture XIX 25

Show

Show for constant acceleration that:

220

2f

Physics 218, Lecture XIX 26

Next Time

• Exam 2 is Thursday!• Bonus Points for getting a 100 on the

mini-practice exam BEFORE the in-class exam

Next week:• Chapter 8HW due Monday morning• Lecture next Thursday will cover

Chapters 9 and 10:– Reading questions due: Q10.7 &

Q10.26

Physics 218, Lecture XIX 27

Computer Hard Drive

A computer hard drive typically rotates at 5400 rev/minute

Find the: •Angular Velocity in rad/sec•Linear Velocity on the rim (R=3.0cm)•Linear AccelerationIt takes 3.6 sec to go from rest to 5400 rev/min, with constant angular acceleration.

•What is the angular acceleration?

Physics 218, Lecture XIX 28

Next Time

• Read Chapter 10– More on angular “Stuff”– Angular kinematics– Torque– Reading questions: Q10.7 & Q10.26

• HW7 Due Monday (released this afternoon)

• Exam 2 next Thursday on Chapters 4-7

Physics 218, Lecture XIX 29

More definitions

•Frequency = Revolutions/sec

radians/sec f = /2

•Period = 1/freq = 1/f

Physics 218, Lecture XIX 30

Motion on a Wheel cont…

A point on a circle, with constant radius R, is rotating with some speed and an angular acceleration . What is the linear acceleration?