Homework 1 Solutions
Problem 1:
Solution:
x
y
2
z2
sinh k cosh k
2
2
cosh 2k
r xi yj zk sinh k i cosh 2k j cosh k k
r k cosh k i 2sinh 2k j sinh k k
r k 2 sinh k i 4 cosh 2k j cosh k k
r k 3 cosh k i 8sinh 2k j sinh k k
So:
s r r
1/2
With
k sin
Due: 09/27/2012 09:30 am (In-class)
09/29/2012 12:00 pm (Distance)
Fall 2012
AEM/ME 562 Homework #2
Note: To obtain credit, you must show your work.
1. The flywheel of the gyroscope rotates about its own axis at 2 = 6,000 rev/min. At the instant when
= 1
Due: 09/18/2012 09:30 am (In-class)
09/20/2012 12:00 pm (Distance)
Fall 2012
AEM/ME 562 Homework #1
Note: To obtain credit, you must show your work.
1. A particle moves along the paraboloid of revolution y x 2 z 2 / , such that x sinh(k ) and
z cosh(k ) ,
Homework 1 Solutions
Problem 1:
Solution:
x
y
2
z2
sinh k cosh k
2
2
cosh 2k
r xi yj zk sinh k i cosh 2k j cosh k k
r k cosh k i 2sinh 2k j sinh k k
r k 2 sinh k i 4 cosh 2k j cosh k k
r k 3 cosh k i 8sinh 2k j sinh k k
So:
s r r
1/2
With
k sin
Due: 10/11/2012 10:45 am (In-class)
10/13/2012 12:00 pm (Distance)
Fall 2012
AEM/ME 562 Homework #3
Note: To obtain credit, you must show your work.
1. Consider the system (shown in the figure below) in a situation where is constant at 2 rad/s, while
is
Due: 09/27/2012 09:30 am (In-class)
09/29/2012 12:00 pm (Distance)
Fall 2012
AEM/ME 562 Homework #2
Note: To obtain credit, you must show your work.
1. The flywheel of the gyroscope rotates about its own axis at 2 = 6,000 rev/min. At the instant when
= 1
Due: 09/18/2012 09:30 am (In-class)
09/20/2012 12:00 pm (Distance)
Fall 2012
AEM/ME 562 Homework #1
Note: To obtain credit, you must show your work.
1. A particle moves along the paraboloid of revolution y x 2 z 2 / , such that x sinh(k ) and
z cosh(k ) ,
Due: 10/11/2012 10:45 am (In-class)
10/13/2012 12:00 pm (Distance)
Fall 2012
AEM/ME 562 Homework #3
Note: To obtain credit, you must show your work.
1. Consider the system (shown in the figure below) in a situation where is constant at 2 rad/s, while
is