PASCO ME-8950A COMPLETE ROTATIONAL SYSTEM - Manual (Page 36)

Complete Rotational System 012-05293F
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where
α is the angular acceleration which is equal to a/r and τ is the torque caused by the
weight hanging from the thread which is wrapped around the base of the apparatus.
where r is the radius of the cylinder about which the thread is wound and T is the tension in
the thread when the apparatus is rotating.
Applying Newton’s Second Law for the hanging mass, m, gives (See Figure 5.3)
Solving for the tension in the thread gives:
Once the linear acceleration of the mass (m) is determined, the torque and the angular
acceleration can be obtained for the calculation of the rotational inertia.
Setup
1. Remove the track from the Rotating Platform and place the
disk directly on the center shaft as shown in Figure 5.4. The
side of the disk that has the indentation for the ring should
be up.
2. Place the ring on the disk, seating it in this indentation.
3. Mount the Photogate/Pulley System to the base and connect
it to a PASCO interface.
4. Attach a thread to the top step of the three-step pulley on the
Rotational Apparatus shaft and suspend the string over the
pulley of the Photogate/Pulley System. Attach a hanger and
mass to the end of the thread.
5. Start the DataStudio program.
Procedure
Measurements for the Theoretical Rotational Inertia
1. Weigh the ring and disk to find their masses and record these masses in Table 5.1.
2. Measure the inside and outside diameters of the ring and calculate the radii R
1
and R
2
. Record in
Table 5.1.
3. Measure the diameter of the disk and calculate the radius R and record it in Table 5.1.
τ
rT =
ΣF mg T – ma = =
T m g a –
( )
=
Figure 5.3: Rotational Apparatus and Free-Body Diagram
rotational disk
"A" base
hanging
mass
mg
T
a
Figure 5.4: Set-up for Disk and Ring
"A" base
mass and
hanger
mass ring
10-spoke pulley with
photogate head
rotational
disk