Physics 101: Lecture 19
Rotational Dynamics

Today’s lecture will cover Textbook Chapter 9
Concept Questions and Example Problems
More on Angular Momentum and Conservation of
Angular Momentum
Physics 101: Lecture 19, Pg 1
See text: chapters 8-9
Angular Momentum
Momentum
Angular Momentum
p=mv
L=I
conserved if Fext = 0
conserved if ext =0
Vector
Vector!
units: kg m/s
units: kg m2/s
See Table 8.1
Physics 101: Lecture 19, Pg 2
Concept Question
You are sitting on a freely rotating bar-stool with your arms stretched out
and a heavy glass mug in each hand. Your friend gives you a twist and you
start rotating around a vertical axis though the center of the stool. You can
assume that the bearing the stool turns on is frictionless, and that there is
no net external torque present once you have started spinning.
You now pull your arms and hands (and mugs) close to your body.
Physics 101: Lecture 19, Pg 3
Concept Question
What happens to your angular momentum as you pull in your arms?
1. it increases
2. it decreases
3. it stays the same
CORRECT
L1
L
2
This is like the spinning skater example in the
book. Since the net external torque is zero (the
movement of the arms and hands involve internal
torques), the angular momentum does not change.
Physics 101: Lecture 19, Pg 4
Concept Question
What happens to your angular velocity as you pull in your arms?
1
1. it increases
CORRECT
2. it decreases
3. it stays the same
2
I2
I1
L
L
as with the skater example given in the book....as you pull
your arms in toward the rotational axis, the moment of
inertia decreases, and the angular velocity increases.
Physics 101: Lecture 19, Pg 5
Concept question
What happens to your kinetic energy as you pull in your arms?
1
1. it increases
CORRECT
2. it decreases
3. it stays the same
2
I2
I1
L
K
1
1 2 2
I 2 
I 
2
2I

1 2
L
2I
L
(using L = I )
Your angular velocity increases and moment of inertia
decreases, but angular velocity is squared, so KE will
increase with increasing angular velocity
Physics 101: Lecture 19, Pg 6
Spinning disks

Two different spinning disks have the same angular momentum,
but disk 2 has a larger moment of inertia than disk 1.
Which one has the biggest kinetic energy ?
(a) disk 1
(b) disk 2
Physics 101: Lecture 19, Pg 7
K
1
1 2 2
I 2 
I 
2
2I

1 2
L
2I
(using L = I )
If they have the same L, the one with the smallest I
will have the biggest kinetic energy.
L  I1 1
L  I2  2
1
2
I1
disk 1
<
I2
disk 2
Physics 101: Lecture 19, Pg 8
Preflights 7 & 8: Turning the bike wheel
A student sits on a barstool holding a bike wheel. The wheel is
initially spinning CCW in the horizontal plane (as viewed from
above). She now turns the bike wheel over. What happens?
1. She starts to spin CCW.
2. She starts to spin CW.
3. Nothing
CORRECT
Physics 101: Lecture 19, Pg 9
Turning the bike wheel...

Since there is no net external torque acting on the studentstool system, angular momentum is conserved.
 Remenber,
L has a direction as well as a magnitude!
Initially: LINI = LW,I
Finally: LFIN = LW,F + LS
LS
LW,I
LW,I = LW,F + LS
LW,F
Physics 101: Lecture 19, Pg 10