Moment of Inertia
PHYS 261 - Lab #9
Objective: Determine the moment of inertia
of various shaped masses and compare with theoretical predictions.
Equipment
-
rotating table
-
ring
-
disk
-
toroidal segment
-
weights
-
smart pulley
-
Science Workshop (use .01511 m rather than .015 as the spoke arc length)
Physical Principles
When a torque is applied to an object it produces an angular acceleration,
a = t/I.
As you will recall, the Parallel Axis Theorem states that Ir
= Icm + mr2 where
Ir = moment of inertia about a point a distance r
from the center of mass
Icm = moment of inertia about the center of mass
Procedure
Be sure the rotating table is level and the string is in a plane before
beginning your experiment. Take data using the smart pulley. Plot velocity
versus time and make sure that the slope is close to constant. The slope
of this plot is the acceleration. Catch the table before the string gets
tangled around its axle, but do not add friction by touching the spinning
table before you stop collecting data. Repeat for several different masses
hung from the end of the string (ie. 50, 75, 100, 125, 150 grams for rotating
table alone, 100, 200, 300, 400, 500, 600 grams for either the disk plus
table or ring plus table or the toroid plus table, 100 to 800 grams in
steps of 100 for the ring plus disk plus table). Plot the torque versus
the angular acceleration. The slope is the moment of inertia. The intercept
is the frictional torque. Moments of inertia are additive, so the moment
of inertia of the table must be determined first, and then subtracted from
the moment of inertia of the system as a whole for the other objects.
Determine the frictional force by dividing the frictional torque by
the radius of the drum.
Determine the following moments of inertia:
rotating table
thick ring
disk
ring and disk
toroidal segment about its center of mass
toroidal segment about an axis removed from the center of mass
Compare your experimental values with theoretical values through integration
for each object.
Are the moments of inertia for your thick ring and disk system additive?
If so, show that IR+D = IR + ID.
If not, why?
The moment of inertia for the toroid should be found by using 6 masses
(100g - 600g) and plotting net versus . The slope of the graph
equals Itoroid.
Demonstrate the validity of the P.A.T. by first measuring Icm
with the center of mass of the toroid centered
on the rotating table. Then shift the position of the toroid out from the
center of the table and redetermine the moment of inertia.
WARNING#$%&!!
When rewinding the rotating table be very careful to keep the string
on the hub. Much precious time has been spent by physics students extracting
string from the rotating table axle.