PASCO ME-9833 Physical Pendulum Set - Manual (Page 5)

Physical Pendulum Set Model No. ME-9833
5
®
Setting Up the Rotary Motion Sensor and Interface
Connect the Rotary Motion Sensor to the interface and connect the interface to a computer. For the
PASPORT Rotary Motion Sensor, connect the sensor’s plug to a compatible PASPORT interface
(e.g., USB Link, PowerLink, Xplorer, Xplorer GLX). For the ScienceWorkshop Rotary Motion
Sensor, connect the yellow plug to digital channel 1 and the black plug to digital channel 2 of a
compatible ScienceWorkshop interface (e.g., ScienceWorkshop 500 or ScienceWorkshop 750).
In general, the set up of the DataStudio program will be for
measuring angular acceleration or for measuring period. To
determine angular acceleration, find the slope of the plot of data on
an angular velocity versus time graph display. To determine period,
use the Smart Cursor to find the time for ten oscillations of the
physical pendulum and then divide the total time for ten oscillations
by ten.
For more information about setting up the DataStudio program, refer
to the Appendix.
Background Information
Pendulum Period
If a body is suspended from a fixed point other than its center of mass and set in motion, it has a
periodic motion that is very nearly simple harmonic motion. The period of
the angular motion depends on the pull of gravity and the moment of inertia
of the body.
For that reason, the physical pendulum is a useful device for determining the
acceleration due to gravity and the moment of inertia. The analytical
relationships for the period, T, are as follows:
for a simple pendulum:
and for a physical pendulum: where
T is the period
L is the length of the simple pendulum
g is the acceleration due to gravity
I is the moment of inertia about an axis through the pivot point
M is the mass of the pendulum, and
L
cg
is the distance from the pivot point to the center of gravity, cg
The first equation is seen to be a special case of the second if ML
cg
2
is substituted for I. These
formulas give good results if the angular amplitude is small.
Torque and Moment of Inertia
For an object accelerating about an axis, the torque is the product of the force and the moment arm
(the distance from the pivot point perpendicular to the line of action of the force):
T 2 π L
g
---- =
T 2 π
I
MgL
cg
------------------ =
Figure 5: Physical
pendulum
θ
mgsin
θ
cg
L
cg
Figure 4: Smart Cursor