Name ___________________________
Section _____________________
ES204
Examination II
January 26, 2009
Problem
Score
1
/30
2
/30
3
/40
Total
/100
Show all work for credit
AND
Turn in your signed help sheet
AND
Stay in your seat until the end of class
The exam is closed-hard-drive. Laptop computers running Maple or other
math software are permitted. Network connections are not allowed.
Mass moment of Inertia of some Common Shapes
Solid Sphere
Ix  Iy  Iz 
z
2 2
mr
5
y
r
G
x
z
Slender Rod
y
1
Iy  Iz 
mL2
12
G
L
x
Solid Circular Cylinder
1
I x  mr 2
2
1
Iy  Iz 
m L2  3r 2
12

z
y
G

r
x
L
Thin Disk
z
1
mr 2
2
1
I y  I z  mr 2
4
Ix 
x
Thin Rectangular Plate

1
m b2  h2
12
1
Iy 
mh 2
12
1
Iz 
mb 2
12
Ix 
y
r
G
z

y
G
h
x
b
Brick



1
m b2  h2
12
1
Iy  m h2  d2
12
1
Iz  m b2  d2
12
Ix 



b
z
y
h
G
d
x
Name
ES204 Examination II
30 pts
Jan. 26, 2009
Problem 1
The “tee” shaped object is released from an unknown position
and pivots on its end. The top of the tee has a mass m1 and
length, w, and the vertical part has a mass m2 and a length, L. If
the bar is about to slip when  = 30 find the angular velocity of
the bar at this instant if s= 0.5. Set-up but do not solve the
necessary equations to find the angular velocity, , of the object.
m1
m2
w

L
DO NOT SOLVE THE RESULTING EQUATIONS! Your
answer should consist of numbered equations and a list of
unknowns. Be sure to clearly document your solution
Name
ES204 Examination II
30 pts
Jan. 26, 2009
Problem 2
During an experiment, a bullet of mass mb unexpectedly passes through a uniform bar of mass m
clipping off part of the bar. A camera records the initial velocity of the bullet to be v1 at an angle
1 and final velocities of the bullet and chip are found to be ( v 2 ,  2 ) and ( v3 ,  3 ) respectively.
The final velocity of point C (the center of gravity of the original bar) is vC . Set-up but do not
solve the necessary equations to find the final angular velocities of the remaining length of the
bar and the chip.
DO NOT SOLVE THE RESULTING EQUATIONS! Your answer should consist of numbered
equations and a list of unknowns. Be sure to clearly document your solution
Knowns:
v1, 1, vC ,
v 2 ,  2 , v3 ,
 3 , mb, m,
L
B
B
0.8 L
0.8 L
C
L
mb
v C
C
1
v1
Instant 1
 3
v3
Instant 2
 2
v 2
Name
ES204 Examination II
Problem 3
40 pts
Jan. 26, 2009
Gear A has a mass of 0.5 kg and a radius of gyration of 60 mm, and
gear B has a mass of 0.8 kg and a radius of gyration of 55 mm.
Gear C is fixed. The link is pinned at AB and has a mass of 0.35 kg
and can be treated as a slender rod. The assembly is released from
rest when  = 0° (rod is horizontal) and moves to  = 90° (rod is
vertical pointing down) under the action of gravity and a constant
clockwise torque M = 100 N-m that is applied to link AB. Set-up
but do not solve the necessary equations to determine the angular
velocity of the link in position 2.
DO NOT SOLVE THE RESULTING EQUATIONS! Your answer
should consist of numbered equations and a list of unknowns. Be
sure to clearly document your solution.
M