Description of the experiments – PASCO ME-9833 Physical Pendulum Set User Manual
Page 6
®
Model No. ME-9833
Physical Pendulum Set
6
For the basic setup for measuring moment of inertia shown in Figure 2,
where T is the
tension in the string and r is the radius of the step pulley to which the string is attached. The net
force
is the difference between the tension, T, and the weight, mg, of the hanging
mass. Therefore, the tension, is
where “a” is related to the angular acceleration,
α, by
a = r
α. The torque becomes:
where the angular acceleration is measured by the Rotary Motion Sensor.
Parallel Axis Theorem
For a physical pendulum, the moment of inertia about an axis through the point of suspension can
be found using the parallel axis theorem,
where I
pivot
is the moment of inertia
about the point of suspension, I
cg
is the moment of inertia about the center of mass, m is the mass of
the pendulum, and L
cg
is the perpendicular distance from the pivot point to the center of mass. In
other words, the moment of inertia about a parallel axis is the moment of inertia about the center of
mass plus the moment of inertia of the entire object treated as a point mass at the center of gravity.
Description of the Experiments
1.Parallel axis theorem: Measure the moment of inertia, I
cg
, around the center of gravity of an
object, and the moment of inertia, I
pivot
, around a pivot point of the object that is not through the
center of mass. Confirm that I
pivot
= I
cg
+ ML
2
cg
where m is the mass of the object and L
cg
is the
distance from the pivot point to the center of gravity.
2.Minimum period of a bar: Given a bar of length, L, calculate L
cg
, the distance from the pivot
point to the center of gravity that would give the minimum period of oscillation for the bar.
Measure the distance that gives the minimum period and compare it to the calculated result.
3.Determine moment of inertia: Use the period, T, of a physical pendulum to calculate the
moment of inertia, I. Compare the calculated value to the theoretical value for I.
4.Acceleration due to gravity: Measure the acceleration due to gravity, g, using period, T, moment
of inertia, I, mass, m, and the distance from the pivot point to the center of gravity, L
cg
.
τ
I
α
r
⊥F
=
=
τ
rT
=
ΣF
mg T
–
ma
=
=
T
mg ma
–
=
τ
rT
rmg rma
–
rmg rm r
α
(
)
–
=
=
=
τ
rm g r
α
–
(
)
=
I
pivot
I
cg
ML
cg
2
+
=