Download - Physics 3210
![Page 1: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/1.jpg)
Physics 3210
Week 3 clicker questions
![Page 2: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/2.jpg)
A particle of mass m slides on the outside of a cylinder of radius a. What condition must be satisfied by the force of constraint at the point (angle 0) where the particle leaves the cylinder?
a
A. Qr= mg
B. Qr= mg sin 0
C. Qr= 0
D. Qr= –mg
E. Qr= –mg sin 0
![Page 3: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/3.jpg)
What can you conclude from the following relation?
A.
B.
C.
D.
ii i
x 0x
LL
i i
0x
L
i
0 for all ix
L
ix 0 for all i
r 0L
![Page 4: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/4.jpg)
What can you conclude from the following relation?
A. Nothing.
B. Angular momentum is conserved (for a closed system).
C. Momentum is conserved (for a closed system).
D. Energy is conserved (for a closed system).
E. Lagrangian mechanics is fun.
i
constant for all ix
L
![Page 5: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/5.jpg)
Which of these choices is a valid way to rewrite the following relation?
A.
B.
C.
D.
i ii i i
x x 0x x
L LL
i i i ii
p x p xL
i i i ii
p x p xL
i i i ii
p x p xL
i i i ii
p x p xL
![Page 6: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/6.jpg)
How many of the following statements are true?
1. Momentum is conserved because space is homogeneous.2. Angular momentum is conserved because space is homogeneous.3. Angular momentum is conserved because space is isotropic.4. Momentum is conserved because space is isotropic.5. Energy is conserved because space is homogeneous and isotropic.
A. Exactly one
B. Exactly two
C. Exactly three
D. Exactly four
E. All five
![Page 7: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/7.jpg)
Which of these choices is the correct expression for the time derivative of the Lagrangian of a closed system?
A. B.
C. D.
jj j
dq
dt q
L L
j jj j j
dq q
dt q q
L L L
jj j
dq
dt q
L L
j j
j j j
dq q
dt q q
L L L
![Page 8: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/8.jpg)
Physics 3210
Week 3 - Wednesday clicker questions
![Page 9: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/9.jpg)
How can we rewrite the following expression?
A. B.
C. D.
2
1
t
j j
t
dp q dt ?
dt
2
1
t
j j
t
q p dt 2
1
t
j j
t
p q dt
2
1
t
j j
t
q p dt 2
1
t
j j
t
q p dt
![Page 10: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/10.jpg)
If we know that
what can we say about the terms in parentheses?
A.
B.
C.
D.
2
1
t
j j j jj j jt
H Hp q q p dt 0
q p
j jj j
H HBoth p and q vanish independently.
q p
j jj j
H HThe sum p + q vanishes.
q p
j jj j
H HEither p or q vanishes, but not both.
q p
jj j
j j j
pH HThe ratio p q = .
q p q/
![Page 11: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/11.jpg)
Physics 3210
Week 3 - Friday clicker questions
![Page 12: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/12.jpg)
There has been a request to have the homework due Thursday (instead of Wednesday) to avoid conflicts with other classes. Which would you prefer?
A. Change to Thursday.
B. Stick with Wednesday.
C. I don’t care.
![Page 13: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/13.jpg)
There has been a request to change the course grading so that the lowest of the 3 midterm exam grades is dropped. Which would you prefer?
A. Count all 3 exams.
B. Drop the lowest of the 3 exams.
C. I don’t care.
![Page 14: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/14.jpg)
Hamilton’s canonical equations are:
If the Hamiltonian is independent of pj, which of the following is true?
A.
B.
C.
D.
jj
jj
Hq
p
Hp
q
jq is constant
jq is zero
jp is constant
jp is zero
![Page 15: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/15.jpg)
A particle slides on a helical wire defined by z=kr=const. If we use as the generalized coordinate, what is the generalized momentum p?
A.
B.
C.
D.
2 2 21p m r k
2
p m r k
2 2p m r k
p m
![Page 16: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/16.jpg)
A particle slides on a helical wire defined by z=kr=const. If we use as the generalized coordinate, the generalized momentumWhat is the Hamiltonian of the system?
A.
B.
C.
D.
2pH mgk
2m
2 2p m r k .
2pH mgk
2m
2pH mgk
2m r k
2
2 2
pH mgk
2m r k
![Page 17: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/17.jpg)
An Atwood machine has total free-hanging length of string l connected to two masses m1 (on the left) and m2 (on the right). Use x as a generalized coordinate. What is the generalized momentum p?
A.
B.
C.
D.
21 2
1p m m x
2 m1
m2
x
l-x
1 2p m m x
1 2p m m x
1p m x
![Page 18: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/18.jpg)
An Atwood machine has a Hamiltonian:
What are Hamilton’s equations of motion?
A.
B.
C.
1 2
1 2
px
m m
p m m g
m1
m2
x
l-x
2
1 2 21 2
pH m m gx m gl
2 m m
1 2
1 2
px
m m
p m m g
D.
E.
1 2
1 2
px
m m
p m m g
1 2
1 2
px
m m
p m m g
1 2
1 2
px
m m
p m m g
![Page 19: Physics 3210](https://reader036.vdocuments.net/reader036/viewer/2022082819/56813bd7550346895da4fff9/html5/thumbnails/19.jpg)
An Atwood machine has the following Hamiltonian equations of motion:
How does the system move?
A. x moves with constant gravitational acceleration with effective mass
B. x moves with constant gravitational acceleration with effective mass
C. x moves with constant gravitational acceleration with effective mass
D. x moves with constant velocity
E. x doesn’t change
m1
m2
x
l-x
1 2
1 2
px
m m
p m m g
1 2m m
1 2m m
1 2 1 2m m m m/