homework 07 – JACOBS, AMBER – Due: Mar 18 2008, 1:00 am
1
Question 1, chap 10, sect 10.
part 1 of 1
10 points
Given:
1 hp=746 W
An automobile engine develops a torque
of 500 N m and is rotating at a speed of
2000 rev
/
min.
What horsepower does the engine generate?
Correct answer: 140
.
375
hp (tolerance
±
1
%).
Explanation:
ω
= (2000 rev
/
min)
parenleftbigg
2
π
rad
1 rev
parenrightbigg parenleftbigg
1 min
60 sec
parenrightbigg
= 209
.
44 rad
/
s
.
We have
P
=
τ ω
= (500 N m) (209
.
44 rad
/
s)
= (104720 W)
parenleftbigg
1 hp
746 W
parenrightbigg
= 140
.
375 hp
.
Question 2, chap 11, sect 11.
part 1 of 2
10 points
A child of mass 51
.
6 kg sits on the edge of a
merrygoround with radius 2 m and moment
of inertia 150
.
672 kg m
2
. The merrygoround
rotates with an angular velocity of 1
.
5 rad
/
s.
What radial force does the child have to
exert to stay on the merrygoround?
Correct answer: 232
.
2 N (tolerance
±
1 %).
Explanation:
Basic Concepts:
Conservation of Angu
lar Momentum.
Centripetal Force:
F
=
m
v
2
r
=
m ω
2
r
The force the child needs to exert in the radial
direction to hold on is simply the centripetal
force:
F
=
m
v
2
r
=
m ω
2
r
Question 3, chap 11, sect 11.
part 2 of 2
10 points
The child then walks towards the center of
the merrygoround and stops at a distance
0
.
88 m from the center.
Now what is the
angular velocity of the merrygoround?
Correct answer: 2
.
80966
rad
/
s (tolerance
±
1 %).
Explanation:
When the child moves inward, the moment of
inertia of the system
i
MGR
+
i
child
(the merry
goround plus the child) changes. Therefore,
to conserve angular momentum, the angular
velocity of the system must change.
Specifi
cally:
L
init
=
L
final
(
i
child
+
i
MGR
)
ω
= (
i
child,
2
+
i
MGR
)
ω
2
The moment of inertia of the child is
m r
2
.
Therefore
ω
2
=
m r
2
+
i
MGR
m r
2
2
+
i
MGR
ω .
Question 4, chap 11, sect 11.
part 1 of 1
10 points
If the polar ice caps of the Earth were to
melt, the oceans would be deeper by about
30m.
What effect would this have on the
Earth’s rotation?
1.
It depends on mass.
2.
Faster.
3.
No change.
4.
Slower.
correct
Explanation:
In accord with the conservation of angular
momentum, if mass moves farther from the
axis of rotation, rotational speed decreases.
So the Earth would slow in its daily rotation.
Question 5, chap 11, sect 11.
part 1 of 1
10 points
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homework 07 – JACOBS, AMBER – Due: Mar 18 2008, 1:00 am
2
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 she
is undergoing uniformly accelerated angular
motion.
2.
Her angular speed increases because by
pulling in her arms she creates a net torque in
the direction of rotation.
3.
Her angular speed increases because her
angular momentum increases.
4.
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.
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 Spring '07
 KOPP
 Physics, Angular Momentum, Power, Work, Moment Of Inertia, Rotation, Correct Answer, kg

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