PASCO ME-8930 SMART TIMER - Manual (Page 29)

012–06734A Smart Timer
25
Experiment Four: Rotational Inertia of a Disk and Ring
EQUIPMENT REQUIRED
• Rotating Platform (ME-8951) • Ohaus Triple-Beam Balance (DE-8707) or similar
• Rotational Inertia Accessory (ME-8953) • paper clips (for masses < 1 g)
• Smart Pulley (ME-9387) • calipers
• Smart Timer (ME-8930)
Purpose
The purpose of this experiment is to find the rotational inertia of a ring and a disk
experimentally and to verify that these values correspond to the calculated theoretical values.
Theory
Theoretically, the rotational inertia, I, of a ring about its center of mass is given by:
where M is the mass of the ring, R
1
is the inner radius of the ring, and R
2
is the outer radius of the ring. See Figure 4.1a.
The rotational inertia of a disk about its center of mass (Figure 4.1b) is
given by:
where M is the mass of the disk and R is the radius of the disk. The
rotational inertia of a disk about its diameter (Figure 4.1c) is given by:
I = 1
2
MR
2
I = 1
4
M R
2
I = 1
2
M(R
1
2
+ R
2
2
)
Figure 4.1b
Disk rotating about its center of mass
Figure 4.1c
Disk rotating about its diameter
R
1
R
2
Figure 4.1a
Definition of R
1
and R
2
of a ring