1. Physics 218 Lecture 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 Schedule This 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 1
Week 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 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!
Chapters 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) = -wR
 Velocity of bike (in ground frame) = wR
Physics 218, Lecture XIX

10. Bicycle comes to Rest
A 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:
What is the angular velocity at t0=0?
Total revolutions before it stops?
Total angular distance traversed by the wheel?
The angular acceleration?
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 w 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 R
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 = 2pr/T
Note: The time to go around once is known as the Period, or T
Physics 218, Lecture XIX

15. The Trick To Solving Problems
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, Q, should the road be banked so that no friction is required?
Physics 218, Lecture XIX

17. Skidding on a Curve
A 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 Pendulum
A small ball of mass m is suspended by a cord of length L and revolves in a circle with a radius given by r = LsinQ.
What is the velocity of the ball?
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. End of Lecture Notes
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.
What is the centripetal acceleration?
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 for constant acceleration that:
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 Acceleration
It 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 Exam 2 next Thursday on Chapters 4-7
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. w radians/sec  f = w /2p More definitions Frequency = Revolutions/sec
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 w and an angular acceleration a.
What is the linear acceleration?
Physics 218, Lecture XIX