PASCO ME-8960 DEMONSTRATION GYROSCOPE - Manual (Page 12)

8
Demonstration Gyroscope 012-05327B
Since d
φ
/dt =
Ω
, the precession speed,
mgd = L
Ω
and the precession rate is given by
Ω
=
mgd
I
ω
where I is the rotational inertia of the disk and
ω
is the angular speed of the disk.
To find the rotational inertia of the disk experimentally, a known torque is applied to the
disk and the resulting angular acceleration is measured. Since
τ
= I
α
,
I =
τ
α
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 pulley on the disk.
τ
= rF
where r is the radius of the pulley about which the thread is wound and F is the tension in
the thread when the disk is rotating.
Applying Newton’s Second Law for the hanging mass, m, gives (See Figure 1.2)
Σ
F = mg – F = ma
Solving for the tension in the thread gives
F = m (g – a)
α
mg
F
pulley
rotating disk
hanging
mass
Figure 1.2: Rotating Disk and Free-Body Diagram