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____________________________________
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01T
Fall Term 2004
InClass Problems 1113: Uniform Circular Motion Solutions
Section ______
Table and Group Number ______________________
Names
____________________________________
Hand in one solution per group.
We would like each group to apply the problem solving strategy with the four stages (see
below) to answer the following two problems.
I.
Understand – get a conceptual grasp of the problem
II.
Devise a Plan  set up a procedure to obtain the desired solution
III.
Carry our your plan – solve the problem!
IV.
Look Back – check your solution and method of solution
1
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View Full Document InClassProblem 11: Whirling Objects
Two objects of equal mass
m
are whirling around a shaft with a constant angular
velocity
ω
. The first object is a distance
d
from the central axis, and the second object is
a distance 2
d
from the axis. You may assume the strings are massless and inextensible.
You may ignore the effect of gravity. Find the tensions in the two strings.
As you begin this problem, consider what types of force diagrams you may need. In
particular what body or system of bodies will use for your free body diagram. It never
hurts to draw as many free body diagrams as you can.
Solution:
Free Body Diagrams: force diagrams for each object.
v
Newton’s Second Law,
F
=
m
1
a
v
, in the radial direction for the inner object is
1
1
2
−=
−
m
d
.
r
ˆ :
TT
1
2
v
Newton’s Second Law,
F
=
m
1
a
v
, in the radial direction for the outer object is
1
1
r
ˆ :
−
m
(2
d
)
.
2
2
T
We can now solve for the tension in the string between the inner object and the outer
object. From the force equation for outer object, the tension in the string between the
inner object and the outer object is
2
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This note was uploaded on 04/22/2011 for the course PHYS 1441 taught by Professor White during the Spring '08 term at UT Arlington.
 Spring '08
 WHITE
 Physics, Circular Motion, Mass

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