I can . . .
• compare
linear inertia
to
rotational inertia
.
• explain how the distribution of mass affects
the amount of
rotational inertia
an object
has.
• apply
rotational inertia
to everyday
phenomena.
• identify the relationship between
rotational
Inertia
An object’s resistance to “
changes in motion
”.
Rotational Inertia
An object’s resistance to “
changes in rotational motion
”.
An object’s resistance to “
acceleration
”.
An object’s resistance to “
angular acceleration
”.
The object with the
greatest
rotational inertia
has the
most resistance
to
angular acceleration
.
Two objects with the same
mass
have the same amount of
linear inertia
,
but not necessarily the same
Both have the
same mass!
Both have the
same
inertia
!
They have
Cross Sections of Three Shapes.
Hollow
Disk
(Ring)
Solid
Disk
Solid
Sphere
I =
2
/
5
·m·r
2
I =
1
/
2
·m·r
2
I = 1·m·r
2
Cross Sections of Three Shapes.
Hollow
Disk
(Ring)
Solid
Disk
Solid
Sphere
I =
2
/
5
·m·r
2
I =
1
/
2
·m·r
2
I = 1·m·r
2
Addison-Wesley “Conceptual Physics”
Paul Hewitt
5/10
4/10
2D
D
𝐼
𝑠𝑝 𝑒𝑟𝑒
h
=
2
5
∙ m ∙ r
2
a) 4
b) 8
c) 12
d) 32
How much more Rotational Inertia does the
How much more Rotational Inertia does the
large
sphere
have than the
small sphere
?
𝐼
=
2
5
∙ m ∙ r
2
𝐼
=
2
5
∙ m ∙ r
2
𝐼
=
2
5
∙
(
𝜌
∙
4
3
𝜋
(
2
𝑟
)
3
)
∙
(
2
𝑟
)
2
𝐼
=
2
5
∙
(
𝜌
∙
4
3
∙
𝜋
∙
𝑟
3
)
∙
𝑟
2
𝐼
=
1
∙
8
15
∙
𝜌
∙
𝜋
∙
𝑟
5
𝐼
=
2
5
∙
(
𝜌
∙
4
3
𝜋
8
𝑟
3
)
∙
4
𝑟
2
𝐼
=
32
∙
8
15
∙
𝜌
∙
𝜋
∙
𝑟
5
𝐼
𝑠𝑝 𝑒𝑟𝑒
h
=
2
5
∙ m ∙ r
2
Which axis of rotation
provides the most/least
amount of rotational inertia?
#2
#1
#3
Which axis of rotation
provides the most/least
amount of rotational inertia?
#1
#1
#3
Which ball has more rotational inertia?
Both balls accelerate at the same rate because
the ball with more weight, ALSO has more inertia.
a)
b)
Newton’s 2
nd
Law
Force
=
Mass
·
Acceleration
Torque
Rotational
Inertia
Angular
Acceleration
Linear
Centripetal Force
=
Mass
·
Centripetal Acceleration
Circular
Angular (Rotational)
τ
=
I
∙
α
F
=
m
∙
a
F
c
=
m
∙
a
c
=
·
r
d =
r
sin(
θ
)
r
F
θ
θ
θ
θ
F
d =
r
r
m
g
θ
θ
α
=
(m
2/5 m
g
)
r
sin(θ)
r
2
5
g
sin(θ)
2
r
α
=
s =
r
·
θ
5
g
sin(θ)
2
r
a =
r
·
5
g
sin(θ)
2
a =
d =
r
sin(
θ
)
Sphere
Ring
Disk
5
g
sin(θ)
2
a =
a =
g
sin(θ)
2
g
sin(θ)
1
a =
= 1
g
sin(θ)
= 2
g
sin(θ)
Acceleration
=
Force (weight)
In your own words, explain WHY
(regardless of size or mass)
I can . . .
• compare
linear inertia
to
rotational inertia
.
• apply
rotational inertia
to everyday phenomena.
• explain how the distribution of mass affects the
amount of
rotational inertia
an object has.
• identify the relationship between
rotational inertia
,
=
(
200
–
111
)
(
20.4
+
11.3
)
= 2.81 m/s
2
11.3 kg
·
9.8
111 N
20.4 kg · 9.8
3.00 =
(
T
(
–
11.3
111
)
)
11.3 kg
·
9.8
111 N
a = 3.00 m/s
2
T
3.00(
11.3
) = (
T
–
111
)
3.00(
11.3
) +
111
=
T
11.3 kg
· 9.8
111 N
20.4 kg · 9.8
200 N
T
τ
=
I
∙
α
0.30 m
(
T
·
0.30
)
=
½(
20.4
∙
0.30
2
)
α
(
T
·
0.30
)
=
½(
20.4
∙
0.30
2
)
a/
0.30
T
=
10.2
·
a
T
-
111
=
m
·(-
a
)
10.2
·
a
-
111
=
11.3
·(-
a
)
- 5.16 m/s
2
=
a
s = r·θ
v = r·ω
Legend has it that, while still a student,
Galileo became intrigued by pendulums
when he saw a suspended lamp swinging
back and forth in the city's cathedral.
Timing the swings with his own pulse, the
story goes, he found that the period (the
time in which the pendulum completes one
trip back and forth) is independent of the
arc of the swing. Grasping the importance
of this to timekeeping he later went on to
develop a more accurate form of pendulum
clock
.
g
L
Period
2
2
2
4
g
Period
http://www.schaffter.com/jpg/flywheel.jpg6
http://www.schaffter.com/jpg/flywheel.jpg6
http://www.photolib.noaa.gov/flight/fly00619.htm http://deni.typepad.com/the_beautiful_life/weblogs/
