PASCO ME-8930 SMART TIMER - Manual (Page 30)

Smart Timer 012–06734A
26
I =
τ
α
To find the rotational inertia experimentally, a known torque is applied to the object and the
resulting angular acceleration is measured. Since
t = Ia,
where
a is the angular acceleration, which is equal to a/r, and t is the torque caused by the
weight hanging from the thread that is wrapped around the base of the apparatus.
τ
= rT
where r is the radius of the 3-Step Pulley 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 4.2)
Σ
F = mg – T = ma
Figure 4.2
Rotational Apparatus and Free-Body Diagram
rotational
disk
"A" base
hanging
mass mg
T
a
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.
T = m g – a
Smart Pulley