Mechanics Lecture 15, Slide 1
Your Comments
This seems not horrible!
I think I understand this.
I don't really understand moment of inertia yet. How can I simply glance at two
spinning objects and get a feel for which one has a higher moment of inertia?
I thought moments of inertia were the most difficult concepts. Although I have
seen much of this in high school I still thought it was rather difficult.
I took notes during this prelecture for the first time and I think it helped a lot. I'd
recommend it.
Integrals make physics way easier
I started off the prelecture happy that angular stuff is similar to Kinematics.
Then I got sad because moment of inertia is a foreign language.
I decided to do physics on Unofficial. That's dedication.
URGENT! I would REALLY like to know if Prof. Selen shares a love for the
great sport of RACQUETBALL! A reply to the answer will be most greatly
appreciated (and it would make my morning)
I just want to see Professor Stone swing/spin objects all over the place, like
the British madman he is. He'll probably make us calculate the moment of
Inertia of the London Eye.
Mechanics Lecture 15, Slide 2
The I of the Eye
Mechanics Lecture 15, Slide 3
2nd Exam Next Week
Second midterm is on Wednesday March 19th at 7pm
(covers units 7-14, not the stuff we are doing now)
12 conceptual (3 choice) + 12 calculational (5 choice)
There is no lab next week. You will have discussion but no quiz.
Discussions from 4-9 pm next Wednesday are cancelled.
If this is you, you can go to any other section next week.
Things that will help you prepare:
Practice exams w/ solutions
Unit 17 Checkpoint (opens Friday)
If you need to you should sign up for a conflict exam in your gradebook.
If you have a triple conflict please contact Prof. Stone:
(m-stone5@illinois.edu)
Please make the homework that is not on the test due later in the
day on Friday. I am thankful that the material not on the test is not
due until after the test, but so many of us have multiple
exams/essays throughout that same week. Please give us more time
to complete the homework. 8pm instead of 8am on friday would
make a great difference. Thank you.
HW short, Warmups,
Agile Programming
Mechanics Lecture 15, Slide 5
Physics 211
Lecture 15
Today’s Concepts:
a) Rotational Motion
b) Moment of Inertia
Mechanics Lecture 15, Slide 6
Kinetic Energy & Rotations
Think of a single mass:
w
Mechanics Lecture 15, Slide 7
Summary of Rotations
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 15, Slide 8
Angular Velocity & Acceleration
dw
a=
dt
w
Constant a does not mean constant w
The sign tell is the direction
Mechanics Lecture 15, Slide 9
Clicker Question
A disk spins at 2 revolutions/sec.
What is its period?
A) T = 2 sec
B) T = 2p sec
C) T = ½ sec
Mechanics Lecture 15, Slide 10
Clicker Question
A disk spins at 2 revolutions/sec.
What is its angular velocity?
A) w = 2p
B) w =
p
rad/sec
rad/sec
2
C) w = 4p
rad/sec
Mechanics Lecture 15, Slide 11
CheckPoint
A wheel which is initially at rest starts to turn with a constant angular
acceleration. After 4 seconds it has made 4 complete revolutions.
How many revolutions has it made after 8 seconds?
A) 8
B) 12
C) 16
a
Less than half got this right so lets try again…
Mechanics Lecture 15, Slide 12
CheckPoint Response
After 4 seconds it has made 4 complete revolutions.
How many revolutions has it made after 8 seconds?
A) 8
B) 12
C) 16
a
A) if it makes 4 rounds in 4s, then it will make 8 rounds in 8s..
B) accelerates 4 rpm per 4 seconds, so 4 + 2(4) = 12.
C) Time is squared- so quadruple the rotations
Mechanics Lecture 14, Slide 13
Calculating Moment of Inertia
Depends on
rotation axis
Is it true that masses which are further away form the
axis of rotation have the greatest moment of inertia?
A) Yes
B) No
Mechanics Lecture 15, Slide 14
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
About half got this right
so lets try again…
c
Mechanics Lecture 15, Slide 15
CheckPoint Response
Which of the following orderings is correct?
A) Ia > Ib > Ic
B) Ia > Ic > Ib
C) Ib > Ia > Ic
a
r
b
r
c
A) Ia = 8mr^2 Ib = 3mr^2 Ic = 2mr^2
B) Ia = 8mr^2 Ib = 3mr^2 Ic = 4mr^2
Mechanics Lecture 15, Slide 16
Calculation Moment of Inertia
…are we supposed to
know how to derive the
moments of inertia for
all of the shapes seen in
the prelecture? That got
pretty technical
I is bigger when
the mass is
further out
Mechanics Lecture 15, Slide 17
Clicker Question
In both cases shown below a hula hoop with mass M and radius R is
spun with the same angular velocity about a vertical axis through its
center. In Case 1 the plane of the hoop is parallel to the floor and in Case
2 it is perpendicular.
In which case does the spinning hoop have the most kinetic energy?
A) Case 1
B) Case 2
C) Same
Case 1
Case 2
R
R
w
w
Case 2 in "Rotating Hoop" looked like a dancing oval man.
Mechanics Lecture 15, Slide 18
In which case does the spinning hoop have the most kinetic energy?
A) Case 1
B) Case 2
C) Same
Case 1
Case 2
R
w
1 2
K = Iw
2
R
w
A) The mass is concentrated farther from the axis in Case 1, so it has a
higher moment of inertia; thus, more kinetic energy.
C) Since the hoops have the same mass, radius, and angular velocity, they
have the same kinetic energy..
Mechanics Lecture 15, Slide 19
Clicker Question
A mass M is uniformly distributed over the length L of a thin rod.
The mass inside a short element dx is given by:
A) M dx
B) dx
M
x
M
M
dx
C)
L
dx
L
L
dx
D)
M
Everything was fine until lambda was
introduced. Then I was lost.
Mechanics Lecture 15, Slide 20
Clicker Question
A mass M is uniformly distributed over the length L of a thin rod.
The contribution to the rod’s moment of inertia about an axis
through its center provided by element dx is given by:
M
A) x
dx
L
2
B)
1 M
dx
2
x L
axis
x
M
dx
L
C)
M 2
dx
L
Mechanics Lecture 15, Slide 21