Announcements. CAPA #11 due this Friday at 10 pm Reading: Finish Chapter 8, Start Chapter 9.1-9.4 Section – this week Lab #4: Rotations Midterm Exam #3 on Tuesday November 8 th , 2011 details given in class on Wednesday practice exam and solutions on CULearn - PowerPoint PPT Presentation
Slide 1
Announcements
CAPA #11 due this Friday at 10 pm
Reading: Finish Chapter 8, Start Chapter 9.1-9.4
Section this week Lab #4: Rotations
Midterm Exam #3 on Tuesday November 8th, 2011
details given in class on Wednesday
practice exam and solutions on CULearn
formula sheet to be posted on web page
Fraction of all clicker questions answered posted on CULearn.
Email me with your clicker ID, name, student ID if you believe it
is incorrect.
Which has a larger moment of inertia?
IA > IBB) IA < IB
C) IA = IBD) Impossible to tell.
Clicker Question
Room Frequency BA
Consider two masses each of size 2m at the ends of a light rod
of length L with an axis of rotation through the center of the rod.
The rod is doubled in length and the masses are halved.
A bar has four forces, all of the same magnitude,
exerted on it, as shown.
What is the sign of the net torque about the axis of
rotation?
Use the sign convention shown.
Clicker Question
Room Frequency BA
A) torque is zero B) positive (+) C) negative ()
tnet = + (F)(L) + (F)(L/2) + (F)(L/2) (F)(L) = +FL
Rotational Kinetic Energy
Does this object have translational kinetic energy?
No, zero net translational velocity of the object.
However, there is motion of each piece of the object and thus
there must be kinetic energy.
Each piece of the donut has a velocity v = w r.
KE = mv2 = m (w r)2
KE = I w2
Rotational KE
Rolling Kinetic Energy
Translation
Rotation
KE (total)
= KE (translation) + KE (rotation)
KEtotal = mv2 + I w2
Both pieces in units of Joules.
* Rolling without slipping means v = w r.
One revolution Dq=2p leads to displacement of 2pr
Which object has the largest total
kinetic energy at the bottom of the ramp?
A) Sphere B) Disk C) HoopD) All the same.
Clicker Question
Room Frequency BA
M
All have the same total KE.
Which has the greater speed at the bottom of the ramp, the
sphere that rolls down the ramp or a block of the same mass that
slides down the ramp?
(Assume sliding friction is negligible)
A) BlockB) SphereC) Both the same
Clicker Question
Room Frequency BA
Block
Sphere:
Hoop:
Disk:
Who wins the race to the bottom sphere, disk, hoop?
Smallest moment of inertia I
will have the largest translational
velocity at the bottom.
Which object will go furthest up the incline?
A) PuckB) DiskC) HoopD) Same height.
The hoop has the largest moment of inertia, and therefore
the
highest total kinetic energy.
H
Clicker Question
Room Frequency BA
Recall:
Momentum p = mvL = IAngular momentum
Relation to force F = p/t = L/tRelation to torque
No external force p = 0L = 0No external torque
(momentum is conserved)(angular momentum is conserved)
Ii i = If f
Conservation of Angular Momentum
Li = Lf
Ii large
i small
Ii small
i large
By changing the distribution of mass,
the moment of inertia is changed.
By conservation of angular momentum,
the angular velocity is therefore modified.
Conservation of L:
I1 large
1 small
By changing the distribution of mass, the moment of inertia is
changed.
By conservation of angular momentum, the angular velocity is
therefore modified.
Conservation of L:
I2 small
2 large
I3 large
3 small
I
=
m
i
r
i
2
i
I
B
=
2
m
L
2
I
A
=
2
(
2
m
)
L
2
2
=
m
L
2
K
E
t
o
t
=
1
2
M
v
2
+
1
2
I
w
2
I
s
p
h
e
r
e
=
2
5
M
R
2
I
h
o
o
p
=
M
R
2
I
d
i
s
k
=
1
2
M
R
2
f
f
i
i
PE
KE
PE
KE
+
=
+
0
0
+
=
+
f
KE
MgH
MgH
KE
f
=
0
2
1
2
1
0
2
2
+
+
=
+
w
I
Mv
MgH
+
=
2
2
2
2
1
2
1
R
v
I
Mv
MgH
+
=
2
2
2
1
R
I
M
v
MgH
2
MR
I
MgH
R
v
+
=
gH
MR
MR
MgH
R
v
7
10
5
2
2
2
=
+
=
v
s
p
h
e
r
e
=
1
0
7
g
H
0
2
1
0
2
+
=
+
Mv
MgH
gH
v
2
=
v
h
o
o
p
=
g
H
v
d
i
s
k
=
4
3
g
H
gH
v
7
10
=
I
h
o
o
p
=
M
R
2
,
I
d
i
s
k
=
1
2
M
R
2
f
f
i
i
PE
KE
PE
KE
+
=
+
MgH
r
v
I
Mv
=
+
2
2
2
1
2
1
L
=
I
w
t
=
D
L
D
t
I
i
w
i
=
I
f
w
f
(
i
f
F
e
x
t
=
0
)
final
initial
L
L
=
f
f
i
i
I
I
w
w
=
i
f
i
f
I
I
w
w
=
