Physics laboratory report #2 by John Sandström ET-3
MOMENT OF INERTIA – ROTATIONAL MOTION OF A RIGID BODY
Introduction
The moment of inertia is a measure of the inertia that a body exhibits when a torque acts on it
causing a change of its rotational motion.
Purpose
Determining the moments of inertia of rotationally symmetric bodies from their period of
oscillation on a torsion axle. Comparing the periods of oscillation of the bodies with different
masses.
Theory
The moment of inertia of a solid body with density ρ(r) with respect to a given axis is defined
by the volume integral
where r┴ is the perpendicular distance from the axis of rotation.
Equipment
1 torsion axle
1 stand base
Cylinder blocks (3pcs) with different mass (m) and radius (r)
Procedure
The transverse rod was fixed in a certain position and the spring was given a potential energy
after a rotation of 180 degrees of the rod. The force (F) was measured with a dynamometer.
Time measurements were taken of the different rotational speeds of the cylinder blocks
which have a different mass and diameter.
Measurements
The table below show the results of oscillations and for various distances (r) between the
torsion axle and the blocks.
r
0.1
0.15
0.2
0.3
F
0.77
0.52
0.4
0.27
τ= rF
0.77
0.078
0.8
0.081
κ= τ / θ κ
0.0245 0.0251
0.0248
0.0255
0.0258
Results
The period of oscillation of a transverse rod with weights is depending on the mass and
diameter of the block and how much the spring is energised. The radius from the central axle
is also affecting the results. Se table below:
plate
plate cylinder
T
0.52 s
0.86 s
I(experimental)
I(theoretical)
Formula
172*10^6
470*10^-6
cylinder 5
plate cylinder
Cylinder 6
1.08 s
298*10^-6
303*10^-6
I=0.5*mr^2
742*10^-6
Cylinder 4
1.83 s
570*10^-6
594.7*10^-6
I=0.5m(r^2at+r^2m)
2.13*10^-3
2.62*10^-3
I=0.5mr^2
Conclusion
I have now studied the moment of inertia and though this experiment gained new knowledge
in this field. In particular interest was the fact that the period of oscillation of a body on a
torsion axle is determined by the moment of inertia and not by the mass of the body.