EXPERIMENT 11. ROTATIONAL DYNAMICS
3. Moment of inertia. The moment of inertia can be calculated from
I
=
τ
α
with uncer
tainty
δI
=
I
r
±
δτ
a
τ
a
²
2
+
(
δα
α
)
2
. Compute your experimental value for the inertia of
the disk from the applied torque found in step 2 and the acceleration found in step 9
of the procedure and compare it to the calculated value found by summing that of the
pulley (disk) and the bar:
I
disk
=
1
2
m
d
r
2
d
and
I
bar
=
1
12
m
b
(
L
2
+
w
2
)
2
. Do these values
agree within the experimental uncertainty?
4. Finally, check the workenergy relation, which state the total work done on a system
equals the change in kinetic energy. There are two forces (gravity and friction) that
do work on the system as the disk is spinning up:
W
g
=
mgh
where
h
= Δ
θr
is the
height the load mass fell while the spool was unwinding, and
W
f
=

τ
f
Δ
θ
, where
τ
f
=

I
Δ
α/
2

. The change in kinetic energy also has two terms (one for the rotation
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