Physics 2111
Unit 14
Today’s Concepts:
a) Rotational Motion
b) Moment of Inertia
Mechanics Lecture 14, Slide 1
Summary of Rotations
x
dx/dt = v
q
w = dq/dt
dv/dt = a
a = dw/dt
Mechanics Lecture 14, Slide 2
Rotational  Translational
Angular velocity w is measured in radians/sec
Frequency f is measured in revolutions/sec
1 revolution = 2p radians
w = 2p f
Period T = 1/f
2p
w=
T
Mechanics Lecture 14, Slide 3
Example 14.1 (LP Record)
If you have an old LP record
that’s rotating at 33 1/3 rpm,
what is w in rad/sec?
If you turn off the turntalbe and
it completes two revolutions
before coming to a stop, what is
a?
Mechanics Lecture 14, Slide 4
Another Summary
dw
a=
dt
at = Ra
v = wR
v2
ac = = w 2 R
R
w
Constant a does not mean constant w
Mechanics Lecture 14, Slide 5
Example 14.2 (Lady bug’s acceleration)
A ladybug is sitting on the edge
of Dr. Carter’s Bruce Springsteen
record album (r=25cm). The album starts from
rest and uniformly accelerates up to its final wf
of 4rad/sec over a period of 5 seconds.
What is atot of the ladybug 2 seconds after the
record started to move?
What is atot of the ladybug 4 seconds after the
record started to move?
Mechanics Lecture 14, Slide 6
summary so far
x
q
dx/dt = v
dq/dt = w
dv/dt = a
dw/dt = a
m
??
Mechanics Lecture 14, Slide 7
Example 14.3 (MOI of mass on rod)
What is the moment of inertia of a
2kg mass attached to a 15cm rigid
massless rod if it is rotated about
the far end of the rod?
What if a second rod/mass
combination is added?
Mechanics Lecture 14, Slide 8
CheckPoint
A triangular shape is made from identical balls and
identical rigid, massless rods as shown. The moment of
inertia about the a, b, and c axes is Ia, Ib, and Ic
respectively.
Which of the following orderings is correct?
A) Ia > Ib > Ic
B) Ia > Ic > Ib
a
C) Ib > Ia > Ic
b
Only about half got this right
so lets try again…
c
Mechanics Lecture 14, Slide 9
CheckPoint Response
Which of the following orderings is correct?
A) Ia > Ib > Ic
a
B) Ia > Ic > Ib
b
C) Ib > Ia > Ic
c
Ia = 8mr2 Ib = 3mr2 Ic = 4mr2
Mechanics Lecture 14, Slide 10
Calculation Moment of Inertia
Bigger when
the mass is
further out
Mechanics Lecture 14, Slide 11
Example 14.4 (MOI of rod)
What is the moment of inertia of
a 10kg rod, 0.5m in length,
rotated about one end?
What if it is rotated about its
center?
Mechanics Lecture 11, Slide 12
Example 14.5 (MOI of rod and mass)
What is the moment of inertia of
10kg rod if a 29kg mass is
attached and it is rotated about
the far end?
What if it is rotated about the
near end?
Mechanics Lecture 11, Slide 13