Physics 101: Lecture 13 Rotational Kinetic Energy and Inertia

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Physics 101 Lecture 13Rotational Kinetic
Energy and Inertia
Exam II

• Todays lecture will cover Textbook Chapter
  8.1-8.2 with a review of circular motion from
  chapter 5
  

OK, this has nothing to do with the above
questions....WHY IS THIS CLASS SO HARD? WHY WHY
WHY Talk to the Prof. Tuesday 130 500 pm 3
07 Loomis
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Lecture Request
I'll be honest, I didn't read any of this, I just
spent 5 hours in the emergency room being poked
with needles. I want to sleep!! PS If you can ask
people during lecture to be quiet it would be
appreciated
I'm really sick of having people all around
me having side conversations. I'm tempted not to
go to lecture anymore because I feel like I learn
nothing when I'm there because people dont know
how to just be quiet.
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Overview of Semester

• Newtons Laws
• S F m a
• Work-Energy
• S F m a multiply both sides by d
• S W DKE Energy is conserved
• Useful when know Work done by forces
• Impulse-Momentum
• S F m a multiply both sides by Dt
• S I Dp Momentum is conserved
• Useful when know about EXTERNAL forces
• Works in each direction independently

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Linear and Angular

• Linear Angular
• Displacement x q
• Velocity v w
• Acceleration a a
• Inertia m I
• KE ½ m v2
• N2L Fma
• Momentum p mv

Today!
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Energy ACT

• When the bucket reaches the bottom, its
  potential energy has decreased by an amount mgh.
  Where has this energy gone?
  
• A) Kinetic Energy of bucket
• B) Kinetic Energy of flywheel
• C) Both 1 and 2.

At bottom, bucket has zero velocity, energy must
be in flywheel!
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Rotational Inertia I

• Tells how much work is required to get object
  spinning. Just like mass tells you how much
  work is required to get object moving.
  
• Ktran ½ m v2 Linear Motion
• Krot ½ I w2 Rotational Motion
• I S miri2 (units kg m2)
• Note! Rotational Inertia depends on what you are
  spinning about (basically the ri in the equation).

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Rotational Inertia Table

• For objects with finite number of masses, use I
  S m r2. For continuous objects, use table below.

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Merry Go Round
Four kids (mass m) are riding on a (light)
merry-go-round rotating with angular velocity w3
rad/s. In case A the kids are near the center
(r1.5 m), in case B they are near the edge (r3
m). Compare the kinetic energy of the kids on the
two rides.
B
A
A) KA KB B) KA KB C) KA

KE 4 x ½ m v2

4 x ½ m w r2 ½ I w2 Where I
4 m r2

Further mass is from axis of rotation, greater KE
it has.

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Contest!
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Inertia Rods

• Two batons have equal mass and length.
• Which will be easier to spin
• A) Mass on ends
• B) Same
• C) Mass in center

I S m r2 Further mass is from axis of
rotation, greater moment of inertia (harder to
spin)
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Rolling Race (Hoop vs Cylinder)

• A hoop and a cylinder of equal mass roll down a
  ramp with height h. Which has greatest KE at
  bottom?
  
• A) Hoop B) Same C) Cylinder
• 25 45 30

they both start with the same potential energy
so they have to end with the same kinetic energy
b/c of conservation of energy. thanks for your
time, have a nice day...I need some of that 90
proof chocolate today!
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Preflight Rolling Race (Hoop vs Cylinder)

• A hoop and a cylinder of equal mass roll down a
  ramp with height h. Which has greatest speed at
  the bottom of the ramp?
  
• A) Hoop B) Same C) Cylinder
• 29 23
  47

I think that cylinder will get to the bottom
first because inertia for a cylinder is less than
that for a hoop type object.
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Good Preflight Responses
I can't think straight because I fell in love!!!
oh How I hope mondays lecture is funny, if not It
will become so! )
I actually don't know, I wanted to say the solid
one would be faster but the answer always seems
to be "the same" in this class.
I am pretty sure that the solid cylinder, having
less rotational inertia, would get to the bottom
first because it would have less built-in
resistance to moving. But these two concepts
don't seem congruous in my head, so... sigh
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Longest Preflight Response
Ok, well I have never had such a hard time with
the preflight before so if I get these questions
right it would have to be a miracle or
something......I think my brain has just decided
to shut down and not work anymore .....oh well,
not like I used it that much anyway...... so yeah
I thought I knew why I put those answers but the
more I think about it the more I really don't
know why I put them and think that I should
change them, so.........yeah..... I think that
for the first one, I was thinking that the hollow
one had more inertia, so i think i was thinking
that it would have a higher kinetic energy
.......and for the bottom one I was thinking that
the solid one would reach it faster since the
hollow one would rotate slower........I really
don't know and I was trying to find things in my
room so I could see if I could reenact the
problem (I know I am stupid, but my brain wasn't
working so I thought I would give my eyes a shot)
but I couldn't find anything with similar radii
and mass and stuff but couldn't so that failed,
and you are probably reading this laughing at me
and not understanding anything I am writing but
it's all good. This is all I can think of at the
moment. (side note in Wednesday's lecture I
really liked the music selection, it was Madonna
if you don't remember, and it totally brought
back some memories when I was a kid and my
sister, who loved Madonna, would do music videos
with our old school video camera that was like
50lbs .....anyways....she and her friends would
always dress up with the big hair and makeup and
lip sing to one of Madonna's songs....well I
really wanted to do one (I guess because I had to
be the pesty younger sibling) but she wouldn't
let me because I was young and didn't know any of
the words to any of the songs, which I didn't but
thought I did to "Material girl", so I BEGGED and
BEGGED for her to let me do one, and my oldest
sister can be pretty mean, but she finally agreed
to let me do it!! Yeah but I didn't know the
words only the chorus, so I have this home video
of me totally looking like an idiot trying to lip
sing to a song I didn't know the words to and
only looking like I was singing the song when it
came to the chorus.....it was great I can't help
but look back and laugh at myself......well I am
glad this entry is so long and entered in late,
so I have no fear of you putting it up in
lecture. But yeah I just thought that I would
commend you on your music selection.......so good
night, see you in lecture!
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Main Ideas

• Rotating objects have kinetic energy
• KE ½ I w2
• Moment of Inertia I S mr2
• Depends on Mass
• Depends on axis of rotation
• Energy is conserved but need to include
  rotational energy too Krot ½ I w2

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Massless Pulley Example

• Consider the two masses connected by a pulley as
  shown. Use conservation of energy to calculate
  the speed of the blocks after m2 has dropped a
  distance h. Assume the pulley is massless.

Note Tension does positive work on 1 and
negative work on 2. Net work (on 1 and 2) by
tension is ZERO.
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Massive Pulley Act

• Consider the two masses connected by a pulley as
  shown. If the pulley is massive, after m2 drops a
  distance h, the blocks will be moving
  
• A) faster than
• B) the same speed as
• C) slower than
• if it was a massless pulley

Slower because some energy goes into spinning
pulley!
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Summary

• Rotational Kinetic Energy Krot ½ I w2
• Rotational Inertia I S miri2
• Energy Still Conserved!
• Practice Problems Ch. 8 3, 5, 9

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