#### Transcript Document

```Lecture series for Conceptual Physics 8th Ed.
Rotational Inertia p118
Alias: momentum of inertia.
The property of an object to resist being rotated
T.R. Walker starts to fall.
So, he pushes
down on his
right and pulls
up on his left to
right himself.
The pole stays
put.
Whose legs have the
least rotational inertia in
fig. 7.3?
Fig 7.5 Rotational inertias of some shapes:
Why does disk beat hoop
down ramp?
Torque p121
Torque = lever arm x force
fulcrum
force
mg
At equilibrium: CCW torque = CW torque
Torque = “la” x F =F x d
Huh?
Fl x dl = Fr x dr
300 x dl=500 x 1.5
dl=2.5m
Center of Mass and Center of Gravity
p123
Fig 7.11 shows the ball
following a smooth
parabola and the bat
wobbling.
In both cases, the CM makes a smooth parabola.
The white dot marks the CM
The CM goes straight!
Center of Gravity
is basically the
same as CM.
Locating the Center of Gravity p 124
Tccw = Tcw
NOTE: The weight of the stick
acts at its center of gravity.
For weird shapes:
For athletes:
Which one is
more stable?
Stability p125
Equilibrium exist when your CG is over your
support.
Whoops!
The amount of stability is determined by how high the CG
must be raised in order to tip the object over.
Most stable
U=mgh?
More Stability
In fig. 7.24 which
has the greater
torque around the
imaginary fulcrum?
This one?
No
This one?
Yes
What contributes to its
greater torque?
Longer
lever arm
Peter Parker
fooling around.
More mass
(force).
Centripetal Force
p128
The force on a moving object that is
directed towards a fixed center.
Is the water forced
away from the
clothes?
No!
The clothes are forced
away from the water.
5g – 1g
Loose mud flies
off on a tangent.
5g + 1g
Centrifugal (the imaginary) force
p129
When the car stops and you’re “thrown” against the
dashboard, you don’t say a force pushed you forward.
You say, “My inertia kept me going and the
dashboard pushed on me.”
The bug wants to go
in a straight line but
the can pushes it
toward the center
Does the bug say, “I’m
pushing on the floor?”
Centrifugal Force in a Rotating Frame p130
The silly bug still thinks that it is in a
stationary can pushing on the floor.
You are lighter
at the equator.
Bugs in the space tire think that
they have “gravity”.
?
Simulated Gravity p 131
A force
toward the
center.
The
action
force
The reaction force
But, this is an
imaginary force.
If the floor were to give way, would he
fly away from the center?
NO!
He would sail off on the tangent.
Angular Momentum
p133
You remember, of course, that linear momentum, p, = m x v.
Since mass and inertia are aspects of the same thing, then you
wouldn’t be surprised that…
AnguLar momentum = rotational inertia x rotational velocity
Given:
=v / r
L=I
(I = mr2 or I = ½ mr2, etc.)
So, L = mr2 v
r
= mvr
What is angular momentum of the ball if
m = 2kg, v = 3m/s and r = 4m?
L=mvr=(2)(3)(4)= 24kg-m2/s
Conservation of Angular Momentum
I
= I
A gymnast balls up to increase
his spin rate.
A falling cat
rotates its
front half to
rotate the
back in the
other
direction,
then
straightens
out for a 4
footed
landing
The end
p134
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