Physics 2015: Rolling Motion and Moment of Inertia
Purpose
 Investigate which factors affect moments of inertia (such
as length, mass, and shape).
 Calculate moments of inertia for various shapes to check
our results.
Physics 2015: Rolling Motion and Moment of Inertia
Equipment
Inclined board on which you can place round objects at the top
of the board and let them accelerate towards the bottom:
Physics 2015: Rolling Motion and Moment of Inertia
Activity I: Data Collection
 Note that for constant acceleration (like in out setup today) the
velocity increases linearly with time. Therefore,
v final  2 v average
where
v avg 
d
t
 To measure vaverage, all you need is a stopwatch (time t) and a ruler
(distance d).
 By the way, the acceleration is
a
v final
t

2 v average
t

2d
t
2
Physics 2015: Rolling Motion and Moment of Inertia
Activity II: Calculating Moments of Inertia
 Simply use conservation of energy, which we quickly see
from the figure below is
1
1
2
2

mgh
mv
2
f
Iw

2
vf
 Since we can’t measure w, we use the fact that w 
r
2
to see that
mgh

1
2
h
mv
2
f
1  vf

I 
2  r




Physics 2015: Rolling Motion and Moment of Inertia
mgh

1
2
mv
2
f
1  vf

I 
2  r




2
 With this equation we can solve for I, which is the moment of inertia of the
rolling object and calculate I from the measured data.
For many round objects I can be calculated as I = Kmr2, where r is the radius,
m is the mass, and K is a number dependent on the mass distribution and
shape.
 To compare your results to theory, write I as I = Kmr2 in the equation above
and then solve the equation for K. Then you will have an expression for K as a
function of g, h, and vf.
 Use this formula to calculate K for three different objects from your measured
data.
 Compare your experimental K-values to those in the literature. (e.g., for a
disk K=1/2 as we saw in the “Rotational Motion” lab” last week).