PASCO ME-9833 Physical Pendulum Set - Manual (Page 25)

Physical Pendulum Set Model No. ME-9833
25
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Appendix D: Teacher’s Notes
Sample Data for Experiment 1: Parallel Axis Theorem
The table shows typical data for the parallel axis theorem using the irregular shape physical
pendulum object. The three columns of data are for the three ‘legs’ of the irregular shape object.
Table 1: Parallel Axis Theorem for Irregular Shape
Questions
1. How does the value of the moment of inertia about the pivot point compare to the sum of the
moment of inertia about the center of gravity plus mL
2
cg
?
The values of the moment of inertia about the pivot point for all three ‘legs’ of the irregular shape
object compare well to the sum of the moment of inertia about the center of gravity plus mL
2
cg
.
2. Do your results confirm the parallel axis theorem? Why or why not?
The results confirm the parallel axis theorem because of the close agreement between measurement
and theory.
Item (units) 1 2 3
Object irregular shape A irregular shape B irregular shape C
Mass of object, M (kg) 0.06339 0.06339 0.06339
Step diameter (m) 0.0298 0.0298 0.0298
Step radius, r (m) 0.0149 0.0149 0.0149
Mass of hanger, m (kg) 0.00512 0.00512 0.00512
α
cg
, avg. angular acceleration
cg
(rad/s 2 )
11.0 11.0 11.0
τ
cg
, torque, rm(g - r α
cg
) (N m) 0.0007347 0.0007347 0.0007347
I
cg
, moment of inertia, center of mass (kg m 2 )
0.00006679 0.00006679 0.00006679
L
cg
, distance - pivot to center of gravity (m) 0.0512 0.0439 0.0350
ML 2
cg
, moment of inertia, parallel axis (kg m 2 )
0.00016610 0.00012216 0.00007765
I
cg
+ ML
2
cg
(kg m
2
)
0.00023289 0.00018895 0.00014444
α
pivot
, avg. angular acceleration
pivot
(rad/s
2
)
3.03 3.78 4.953
τ
pivot
, torque, rm(g - r α
pivot
) (N m) 0.00074417 0.00074332 0.00074199
I
pivot
, moment of inertia, pivot point (kg m 2 )
0.00024560 0.00019717 0.00015050
Percent difference, I
pivot
and I
cg
+ mL 2
cg
5.1% 4.1% 4.0%