Experiment 9: Rotational Dynamics
EXPERIMENT 9: ROTATIONAL DYNAMICS
Objective:
To investigate the relationship between torque and angular acceleration and to verify the work-
energy theorem for rotational motion.
Theory:
The rotational analogue to
r
F =mr
a
is
r
=Ir
where
r
is the torque, I is the moment of inertia
and
r
is the angular acceleration. If we apply a torque to a body that can rotate about a fixed
axis, it will undergo an angular acceleration and a change in its angular velocity. Therefore, its
rotational kinetic energy will increase. The rotational kinetic energy is given by KE = 1/2 I
2 ,
where is the angular velocity (radians per second).
Procedure:
DO NOT ROTATE THE DISK UNTIL AIR PRESSURE IS SUPPLIED
Your instructor will demonstrate proper operation of the apparatus. A steel disk spins about a
vertical axis, supported by a thin layer of air that provides a virtually frictionless support. An
optical scanner counts stripes on the rim to measure the linear speed of the rim. Angular
acceleration is produced by the tension in a cord attached to a small load mass. Although you
will work in groups of two, each student should record his or her own data using a different
value for the small load mass.
1. Being careful not to scratch the air-bearing surface, remove the top disk and measure its mass
and radius. Record these values in a data table. If the sliding surfaces are dirty, clean them
with a chemwipe.
2. Reassemble the system with the thread anchor washer and a small spool attached to the disk
with the thumb screw.
3. With the proper air pressure applied, test the operation of the optical scanner. It counts for
one second, displays for one second, then clears and repeats. The value displayed is related to
the linear speed of the rim which you will convert to angular velocity, as described below.
4. Wind the string around the spool, lifting the small load mass. The first group member should
start with 25g of mass on the hanger and each group member should add an additional 5g
before taking their data. Measure the difference between the height the load starts at and the
height it rises to after falling and coming back up. We’ll call this y, the change in
maximum height and will use this in an energy calculation.
5. Release the system from rest and record the rim speed readings over a 30-second interval.
One partner watches the scanner output and calls out the readings while the other writes
down the data. As the weight falls, the disk will speed up, but when the string is entirely
played out, the string will wind back on the spool, raising the weight and slowing the disk
