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18
TORQUE AND INERTIA
Objective
:
The purpose of this experiment is to study torque in a dynamic situation and obtain a
better understanding of moment of inertia.
Apparatus
: Cenco centripetal force apparatus with moment of inertia accessory, masses,
Computer, Calipers, micrometer, (use short string so mass hangs about 10 cm off the floor).
Background
:
The purpose of this lab is to compare the moment of inertia calculated from rotational
acceleration caused by a known torque to that predicted by the direct moment of inertia
calculation.
The equations describing the motion of rotating bodies under constant torque are
very similar to the equations of motion for constant linear acceleration.
Replacing the mass with
the moment of inertia and also the force with the torque gives the equations for the angular
motion quantities.
So, the sum of all forces on an object,
F
ma
, becomes
I
Eq 1)
where
is the sum of all torques,
I
is the moment of inertia, and
is the angular
acceleration.
The other rotational motion equations are similar to the linear motion equations as
well.
These can be solved for by integrating equation 1.
The results are
0
0
I
t
t
, and
Eq 2)
0
0
2
0
0
2
1
2
1
2
t
I
t
t
t
.
Eq 3)
Linear quantities are related to the circular quantities using the following equations,
d
R
,
Eq 4)
v
R
,
and
Eq 5)
a
R
Eq 6)
where
v
is the speed,
is the angular velocity,
R
is the radius of motion,
d
is the
circumference displacement and
is the angular displacement.
The torque need not be applied at the radius where the masses are located so it is
designated to have a different
r
.
The torque when the force is applied perpendicular to the radius
is given by
Fr
.
Eq 7)
Using the example of a merry go round, one can understand immediately why the r’s can be
different.
The torque need not be applied out where the horses are; it can be applied to a central
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This note was uploaded on 08/25/2011 for the course PHYS 164 taught by Professor Johnjames during the Fall '09 term at MO St. Louis.
 Fall '09
 JohnJames
 Force, Inertia, Mass

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