User's Manual

Complete Rotational System 012-05293F
10
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, and
where r is the radius of the 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 1.2):
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.
For comparison, the initial speed (muzzle velocity) of the ball is determined by shooting the ball
horizontally off the table onto the floor and measuring the vertical and horizontal distances through
which the ball travels.
For a ball shot horizontally off a table with an initial speed, v
o
, the horizontal distance traveled by the
ball is given by x = v
o
t, where t is the time the ball is in the air. No air friction is assumed.
The vertical distance the ball drops in time t is given by .
The initial velocity of the ball can be determined by measuring x and y. The time of flight of the ball
can be found using:
and then the muzzle velocity can be found using v
o
= x/t.
v
0
Iω
m
b
R
----------
=
I
τ
α
---
=
τ rT=
ΣFmgT– ma==
Tmga–()=
y
1
2
---
gt
2
=
t
2y
g
------=
mg
Rotating
Platform
"A" base
hanging
mass
a
Figure 1.2: Rotational Apparatus and Free-Body Diagram
T