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Will we be expected to reproduce the derivation of the equations? Exams are M/C
Talk about precession pretty pretty please!!! It's such a raw, awesome, and difficult
concept. Lecture 20
I'm looking forward to seeing everyone stick on their hands and curl the fingers on
the exam Not on exam 2
When it comes to the right hand rule, I understand the rule but why would the
acceleration, and therefore torque, point in the same direction as the axis of
rotation? For example, in the "torque and the cross product" slide, the acceleration
is out of the screen. Nothing is coming towards us, correct? Today’s topic
In the prelecture's exmaple for calculating moment of intertia for the dumbell, I
still don't understand from where did the 1/12 come... Slide 8 on PL 14
Goodness knows physics isn't my favorite subject, but at least I never fall asleep
during physics lectures!
Let's replicate Felix Baumgartner's awesome space jump and turn it into a
fantastic kinematics demonstration! I volunteer myself to jump. Better not…
I apologize for the lack of time spent on the pre-lecture. As others have said Relax
before, I ran out of time tonight, and so hurriedly completed both the pre-lecture
and checkpoint. I hope my grade does not reflect the abysmal lapse in memory.
Is there anyway that you could have high schools use this prelecture method? It
helps to watch the derivation of the formulas and it definitely beats reading a
book. A few do
Mechanics Lecture 15, Slide 1
I really try so hard to pay attention during these prelectures
because I love it when they teach crazy stuff, but I can only
ever think about stupid things while I watch them...
Try doing them at a different time of day…
Mechanics Lecture 15, Slide 2
Physics 211
Lecture 15
Today’s Concepts:
a) Parallel Axis Theorem
b) Torque & Angular Acceleration
Mechanics Lecture 15, Slide 3
Parallel Axis Theorem
I don't understand what
the parallel thingy really
was or why it is useful
I don't understand what the parallel
thingy really was or why it is useful
Smallest when D = 0
Big Idea is simple:
I is bigger when stuff is further
from the rotation axis.
Mechanics Lecture 15, Slide 4
The parallel axis theorem always confuses me when it comes to
rotating multiple three dimensional objects around an axis that is
not the center of any three dimensional object. Can you talk a little
more about that during lecture?
F
axis
Mechanics Lecture 15, Slide 5
Clicker Question
A solid ball of mass M and radius is connected to a thin rod
of mass m and length L as shown. What is the moment of
inertia of this system about an axis perpendicular to the
other end of the rod?
2
1 2
2
2
A) I = MR  ML  mL
5
3
2
1
2
2
B) I = MR  mL  ML2
5
3
2
1 2
2
C) I = MR  mL
5
3
1
D) I = ML2  mL2
3
R
M
m
L
axis
Mechanics Lecture 15, Slide 6
CheckPoint
A ball of mass 3M at x = 0 is connected to a ball of mass M at x = L by a
massless rod. Consider the three rotation axes A, B, and C as shown, all
parallel to the y axis.
For which rotation axis is the
moment of inertia of the object
smallest? (It may help you to
figure out where the center of
mass of the object is.)
A
C
B
y
x
3M
M
L
since the center of mass is at L/4, the
smallest moment of inertia will be when this
object is rotated about L/4
0 L/4 L/2
Mechanics Lecture 15, Slide 7
Right Hand Rule for finding Directions
Big Idea is simple:
The axis is the only thing that
defines the direction of rotation
Professor Selen, I almost stuck my
head in a bucket of acid with this
prelecture. …The right hand rule
showed that the angular velocity was
perpendicular to the rotation! How is
that even possible if ω=dθ/dt? And the
same with torque, perpendicular, so
coming out of the screen?!!! Thanks!
Mechanics Lecture 15, Slide 8
Clicker Question
A ball rolls across the floor, and then starts up a ramp as
shown below. In what direction does the angular velocity
vector point when the ball is rolling up the ramp?
A) Into the page
B) Out of the page
C) Up
D) Down
Mechanics Lecture 15, Slide 9
Clicker Question
A ball rolls across the floor, and then starts up a ramp as
shown below. In what direction does the angular
acceleration vector point when the ball is rolling up the ramp?
A) Into the page
B) Out of the page
Mechanics Lecture 15, Slide 10
Clicker Question
A ball rolls across the floor, and then starts up a ramp as
shown below. In what direction does the angular
acceleration vector point when the ball is rolling back down
the ramp?
A) into the page
B) out of the page
Mechanics Lecture 15, Slide 11
Torque
can you go over the
torque on the door.
t = rF sin(q )
Mechanics Lecture 15, Slide 12
Torque and F=ma
F = ma
Fq = maq
Fq = mr
 rFq = mr 
 r  F = mr 
2
t
=
I


v
F
q
r
2
Mechanics Lecture 15, Slide 13
Look at Prelecture slide 9 again
It’s all there….
Mechanics Lecture 15, Slide 14
How to think of r x F
F
q
q
F
F
q
q
q
r
r  F = rF sinq
r
r
=r(Fsinq)
=F(rsinq)
Mechanics Lecture 15, Slide 15
CheckPoint
In Case 1, a force F is pushing perpendicular on an object a
distance L/2 from the rotation axis. In Case 2 the same force is
pushing at an angle of 30 degrees a distance L from the axis.
In which case is the torque due to the force about the rotation
axis biggest?
A) Case 1
B) Case 2
C) Same
axis
axis
L/2
90o
Case 1
F
L
30o
F
Case 2
Mechanics Lecture 15, Slide 16
CheckPoint
In which case is the torque due to the force about
the rotation axis biggest?
axis
A) Case 1
B) Case 2 C) Same
90o
L/2
F
A) Because the force is
perpendicular
B) the length in 2 is
bigger
C) sin(30)=1/2
Case 1
axis
L
30o
F
Case 2
Mechanics Lecture 15, Slide 17
Similarity to 1D motion
Mechanics Lecture 15, Slide 18
Clicker Question
Strings are wrapped around the circumference of two solid
disks and pulled with identical forces. Disk 1 has a bigger
radius, but both have the same moment of inertia.
Which disk has the biggest angular acceleration?
A) Disk 1
w2
w1
B) Disk 2
C) same
F
F
Mechanics Lecture 15, Slide 19
CheckPoint
Two hoops can rotate freely about fixed axles through their
centers. The hoops have the same mass, but one has twice
the radius of the other. Forces F1 and F2 are applied as
shown.
How are the magnitudes of the two forces related if the
angular acceleration of the two hoops is the same?
A) F2 = F1
B) F2 = 2F1
F2
F1
C) F2 = 4F1
Case 1
Case 2
Mechanics Lecture 15, Slide 20
CheckPoint
How are the magnitudes of the two forces related if the
angular acceleration of the two hoops is the same?
F2
A) F2 = F1
F1
B) F2 = 2F1
M, R
C) F2 = 4F1
Case 1
t = I
M, 2R
Case 2
RF = MR 
F = MR
2
Mechanics Lecture 15, Slide 21
t = R F s in q
q
q = 90 0
q = 00
q = 90  36 = 54
Mechanics Lecture 15, Slide 22
t = R F s in q
Direction is perpendicular to
both R and F, given by the
right hand rule
tx = 0
ty = 0
t z = t F1  t F2  t F3
Mechanics Lecture 15, Slide 23
(i)
1
I DISK = MR2
2
(ii)
t = I
1 2
(iii) K = Iw
2
Use (i) & (ii)
Use (iii)
Mechanics Lecture 15, Slide 24