PASCO ME-9502 Statics System - Manual (Page 72)

S t a t i c s S y s t e m E x p . 1 1 C : S i m p l e H a r m o n i c M o t i o n – B e a m o n a S p r i n g
®
68 012-12876B
where I is the moment of inertia and k is the spring constant. If you assume that the beam is like a rectangular-type
rod, then the moment of inertia about the center of mass of the rod is:
where M is the mass and L is the length of the rod. The Parallel Axis Theorem predicts that the moment of inertia
about an axis at the end of the rod is
where L
cm
is the distance from the center of mass of the rod to the parallel axis (the pivot point).
Of course, any other mass added to the beam would alter the moment of inertia. For example, if a point mass, m, is
at a distance, r, from the pivot point, its moment of inertia is I = mr
2
. The moment of inertia would be the sum.
Procedure
1. Measure and record the mass of the of the Balance Arm beam. Measure and record the mass of a Protractor.
2. Place the Pivot at the 170 mm mark on the Balance Arm beam. Mount the Protractor on the beam at the 110
mm mark. Mount the Balance Arm beam on the Statics Board.
3. Mount the Spring Scale on the Statics Board so that the scale is perfectly vertical. Use thread to connect the
Angle Indicator on the Protractor to the bottom hook of the Spring Scale.
4. Adjust the Balance Arm and the Spring Scale so that the arm is horizontal and the scale is directly above the
center of the protractor.
5. Push the Balance Arm beam down to a small angle (less than 20°) and release it smoothly. Measure the time
for ten complete oscillations (or as many oscillations as possible). Record the number of oscillations and the
total time.
6. Calculate and record the Measured Period, T
measured
, by dividing the total time by the number of oscillations.
7. Repeat the measurement for the first position of the Protractor five times.
8. Change the position of the Protractor by moving it 10 millimeters (mm) farther away from the pivot point and
repeat the measurements.
9. Repeat the procedure for 90 mm, 80 mm, and 70 mm for a total of five distances.
I
cm
1
12
------ML
2
=
I
parallel
I
cm
ML
cm
2
+
1
12
------ML
2
ML
cm
2
+ = =
Spring
Scale
Pivot
base
Protractor
Figure 11.7: Equipment Setup
Thread
Center of
mass
Balance Arm
beam