midterm 04 – – Due: May 2 2007, 11:00 pm
1
Question 1, chap 1, sect 1.
part 1 of 1
7 points
A 3 m long rod of negligible weight is at
tached on one end to a ball joint which allows
the rod to rotate in all directions.
The free
end of the rod points 30
◦
above the Eastward
horizontal direction.
A 50 N force directed
vertically Down is applied at the rod’s free
end.
What is the direction of the torque due to
this force (relative to the pivot end of the
rod)?
1.
Horizontally Southward
2.
Down and Eastward
3.
Vertically Up
4.
Insufficient data to determine the direc
tion.
5.
Horizontally Westward
6.
Horizontally Eastward
7.
The torque vanishes
8.
Horizontally Northward
correct
9.
Vertically Down
10.
Up and Southwest
Explanation:
Use the right hand rule for
vector
τ
=
vector
X
×
vector
F
:
Stick your right thumb parallel to the rod —
diagonally upward of East — and let your
fingers point in the direction of the force —
vertically Down.
Consequently, the plain of
your hand is vertical and your palm faces
horizontally Northward.
Alternatively, you may use a right coordi
nate system:
the
x
axis points East, the
y
axis point North and the
z
axis points Up.
In terms of the unit vectors ˆ
ı
, ˆ
and
ˆ
k
, we
have a force
vector
F
=

F
ˆ
k
acting at the location
vector
X
= (
L
cos
θ
)ˆ
ı

(
L
sin
θ
)
ˆ
k
.
Consequently,
the torque
vector
τ
=
vector
X
×
vector
F
=

FL
cos
θ
(ˆ
ı
×
ˆ
k
) +
FL
sin
θ
(
ˆ
k
×
ˆ
k
)
=

FL
cos
θ
(

ˆ
) +
FL
sin
θ
(0)
= +(
FL
cos
θ
) ˆ
points along the positive
y
axis – horizontally
Northward.
Question 2, chap 13, sect 3.
part 1 of 1
7 points
A figure skater on ice spins on one foot.
She pulls in her arms and her angular speed
increases.
Physically, this happens because
...
?
Choose the reason from the list below; if
two or more reasons seem plausible, choose
the most important reason.
1.
Her angular speed increases because her
potential energy increases as her arms come
in.
2.
Her angular speed increases because air
friction is reduced as her arms come in.
3.
Her angular speed is unrelated to her
arms. She pulls them in at the same time as
she speeds up her spin because it looks better
this way.
4.
Her angular speed increases because she
is undergoing uniformly accelerated angular
motion.
5.
Her angular speed increases because by
pulling in her arms she creates a net torque in
the direction of rotation.
6.
Her angular speed increases because her
angular momentum remains the same but her
moment of inertia decreases.
correct
7.
Her angular speed increases because her
angular momentum increases.
Explanation:
When a skater spins on one foot — or rather
on just the toe of one skate — the external
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midterm 04 – – Due: May 2 2007, 11:00 pm
2
forces acting on her produce no net torque
because of zero lever arms. Consequently, the
skater’s
angular momentum
is conserved,
L
=
Iω
= const
.
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 Spring '08
 Turner
 Frequency, Wavelength, Standing wave, angular speed increases, superposed waves

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