Transcript Physics 218 Lecture 16 Dr. David Toback Physics 218, Lecture XVI

Physics 218
Lecture 16
Dr. David Toback
Physics 218, Lecture XVI
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Rotational Motion
Will do Chapters 9 and 10 in four combined
lectures
• Start with Fixed Axis motion
• The relationship between linear and
angular variables
• Rotating and translating at the same time
• First kinematics, then dynamics
– just like earlier this semester
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Overview: Rotational Motion
• Take our results from “linear” physics
and do the same for “angular” physics
• We’ll discuss the analogue of
– Position
– Velocity
– Acceleration
– Force
– Mass
– Momentum
– Energy
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Rotational Motion
• Here we’re talking about stuff that
goes around and around
• Start by envisioning:
A spinning object
like a car tire
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Some Buzz Phrases
• Fixed axis: I.e, an object spins in the
same place… an ant on a spinning top
goes around the same place over and
over again
Another example: Earth has a fixed
axis, the sun
• Rigid body: I.e, the objects don’t
change as they rotate. Example: a
bicycle wheel
Examples of Non-rigid bodies?
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Overview: Rotational Motion
– Position
←
– Velocity
←
– Acceleration ←
– Force
– Mass
– Momentum
– Energy
Start
here!
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Chapters 1-3
• Take our results from “linear” physics and do the
same for “angular” physics
• Analogue of
7
Axis of Rotation: Definitions
Pick a simple
place to
rotate
around
Call point O
the “Axis of
Rotation”
Same as
picking an
origin
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An Important Relation: Distance
If we are sitting
at a radius R
relative to our
axis, and we
rotate through
an angle q,
then we travel
through a
distance l
l  θR
Circ  2R
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Velocity and Acceleration
Define  as the angular ve locity
q
dq

or  
radians/ sec
t
dt
Define  as the angular accelerati on
2
d
dq
2

or   2 radians/ sec
dt
dt
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Motion on a Wheel
What is the
linear speed of a
point rotating
around in a
circle with
angular speed
, and constant
radius R?
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Examples
Consider two points on a
rotating wheel. One on
the inside (P) and the
other at the end (b):
•Which has greater
angular speed?
•Which has greater
linear speed?
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b
R1
R2
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Uniform Angular Acceleration
Derive the angular equations of motion
for constant angular acceleration
1 2
  0 0t  t
2
  0  t
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Rotation and Translation
Objects can both translate and rotate at the
same time. They do both around their center
of mass.
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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?
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Derivation
• The trick is to pick your
reference frame correctly!
• 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
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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:
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?
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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?
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Show
Show for constant acceleration
that:
    2q
2
f
2
0
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Exam 2
• Class average for the 2nd exam (including the 5
points) was 80.1%
– Average for first two exams is a 78.7%
• Straight scale for curve for now
• 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
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Next Time
• Lecture on Thursday will cover
Chapters 9 and 10:
–Reading questions due: Q10.7 &
Q10.26
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Next Time
• Exam 2 is Thursday!
• Bonus Points for getting a 100 on the minipractice 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
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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
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More definitions
• Frequency = Revolutions/sec
 radians/sec  f =  /2
• Period = 1/freq = 1/f
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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?
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