physics 218, lecture xix1 physics 218 lecture 19 dr. david toback
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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?