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Review of Quiz 4
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•
•
•
Total: 50
Average: 28.4
High: 47
Low: 5
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Problem 1
• Problem 1 (5 points): Suppose a 7.5kg mass is rotating about an
axis at a distance of 5 m. What is the object’s moment of inertia
about the axis?
a) 38 kg-m2 b)190 kg-m2
c)280 kg-m2
d)400 kg-m2
• Answer:
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Problem 2
• Problem 2 (5 points): What is the vector product of AxB if A=3i
and B=4j?
a) 3i + 4j
b) 0
c) 0.7i
d) 12k
• Answer:
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Problem 3
• Problem 3 (5 points): A post is driven perpendicularly into the
ground and serves as the axis about which a gate rotates. A force
of 12N is applied perpendicular to the gate and acts parallel to the
ground. How far from the post should the force be applied to
produce a torque of 3.0 Nm?
a) 0.25m
b) 4.0m
c) 36m
d) 12 m
• Answer:
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Problem 4
• Problem 4 (5 points): A constant torque of 30Nm is applied to a
merry-go-round for 10 seconds. Neglecting friction what is the
magnitude of the change of the merry-go-round’s angular
momentum?
a)3kg-m2/s b)0.3kg-m2/s c) 300kg-m2/s d) 3kg-m2/s
• Answer:
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Problem 5
• Problem 5 (5 points): A disk of 4.0 kg and 0.20 m is rotating about
its axis of symmetry at w =10 rads/sec. What is the rotational
kinetic energy?
• Answer
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Problem 6
• Problem 6 (10 points): Starting from rest a 5.0kg cylinder of radius
0.5m rolls down an inclined plane without slipping or sliding. How
much will the height of the cylinder have decreased when the
velocity is 10m/s?
+5pts
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Second we are interested in the change of height
1 2 1 2
1
mgh  mv  Iw . For a cylinder w  v / R and I  mR 2 ,
2
2
2
1 2 11
substituti ng, mgh  mv 
MR 2 (v / R) 2 
2
22
1 2 1 2 3 2
mv  mv  mv 
2
4
4
3v 2
3v 2 3(10m / s ) 2
gh 
h

 7.7m  8m +5pts
2
4
4 g 4(9.8m / s )
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Problem 7
Problem 7(15points): As
shown in the figure, a diver
of weight 530 N is poised at
the right end of a diving
board. The board has length
3.90 m. The board has
negligible weight and is
bolted down at the left end
while supported 1.4 m away
by a fulcrum. Draw the
equilibrium diagram with all
three forces involved. Find
the forces F1 and F2 that the
bolt and fulcrum exert on the
board.
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F
y
 0   F1  F2  W   F1  F2  530 N 
F1  F2  530 N
  0 (0) F  l F
1
2
2
 lW W  (1.4m) F2  (3.9m)(530 N ) 
(3.9m)(530 N )
F2 
 1480 N
(1.4m)
+5pts
Substituti ng into the first equation w e have F1  950 N
+5pts
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A Narrative: Where We’ve Been
• Started by describing linear motion with constant
acceleration, free fall, and projectile motion.
• Studied Newton’s 2nd Laws and Law of Gravitation and
saw how these can be quantitatively applied to many
systems.
• Laws naturally lead to concepts of work, energy, and
conservation of energy and momentum.
• Finally applied these to find complete analog to
rotational motion.
• We can now describe the mechanical universe over an
immense range of distances: a top, a hurricane, and a
galaxy. A true achievement and always fun!
• Next semester you’ll carry these tools into
electromagnetism, in particular vector operations, energy
conservation, and potential fields.
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Final
• Comprehensive
• Multiple Choice
– Eight questions
– Five points each
• Problems
– Six Questions
– Points:
• Two Five point questions
• Two Ten point questions
• Two Fifteen point
questions
– Partial Credit Given!
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• Open Book You may
bring my notes as well,
(but that seems like
needlessly killing trees.)
• Calculators will be needed
• All Material Covered:
– Chapters 1-11
– Chapter 12, Sections
1,2,3,4
– Chapter 14, Sections 1,2
• 100 Points
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Computing Grades
• Four quizzes - 50 points each – 200 points maximum.
• Final exam - 100 points - 100 points maximum.
• Unit problem sets - 12 points each, due before quiz – 84
points maximum.
• Fourteen laboratories - 15 points each - 210 points
maximum. (Note: Each student must get 120 points or
more in the laboratory to pass the course, regardless of
other scores.)
• Extra credit – Each problem worth one point. Final extra
credit is equal to the fraction of problems correct times
70 - 70 points maximum.
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Grade Scale
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•
A : 535 or more points
B : 475 to 534 points
C : 416 to 474 points
D : 357 to 415 points
F : less than 357 points
(If necessary may be adjusted for curve)
If you want your grade stop by or send me email!
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Final Exam Topics & Problems
• Unit conversion
• Motion in two dimensions and projectile motion
• Free-body analysis with normal, frictional, and
gravitational forces involved.
• Definition of non-conservative and conservative
forces and examples.
• Definition and application of work for linear
motion
• Conservation of mechanical energy
• Elastic force and energy
• Gravitational force and conservation of energy
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•
Scattering in one dimension
Vector Operations (addition, dot, vector)
Moment of Inertia
A free-body analysis involving forces, torque,
and moments of inertia
• Qualitative understanding of tops and precession
• Calculating the impact of the Coriolis force
• A statics problem involving forces and torques
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