PASCO ME-8950A COMPLETE ROTATIONAL SYSTEM - Manual (Page 29)

012-05293F Complete Rotational System
25
Experiment 4: Conservation of Angular Momentum
Using a Point Mass
EQUIPMENT REQUIRED
- DataStudio Program - Rotating Platform (ME-8951)
- PASCO Interface (see Note) - Photogate/Pulley System
- Rotational Inertia Accessory (ME-8953) - Balance
Purpose
A mass rotating in a circle is pulled in to a smaller radius and the new angular speed is predicted
using conservation of angular momentum.
Theory
Angular momentum is conserved when the radius of the circle is changed
.
where I
i
is the initial rotational inertia and
ω
i
is the initial angular speed. So the final rotational
speed is given by:
To find the rotational inertia experimentally, a known torque is applied to the object and the
resulting angular acceleration is measured. Since
τ = Iα,
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 4.1)
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.
L I
i
ω
i
I
f
ω
f
= =
ω
f
I
i
I
f
--- ω
i
=
I
τ
α
--- =
τ rT =
ΣF
mg T – ma = =
T m g a – ( ) =
Note: If you are
using a PASPORT
interface, you will
also need a Digital
Adapter (PS-2159)