ROTATIONAL INERTIA VIII
DEBRA JONES
PARTNER NAME: JULIA JONES
OCTOBER 28, 2014
PHYSICS-105-004
Abstract:
The purpose of these experiments were to demonstrate how the size, shape, and mass
distribution of an object affects the motion of a rotational system. The first part of the experiment
tested was how the distribution of mass affected the rotational motion. This was done by placing two
weights at three different sets of radii and measuring their rotational inertia by using a rotary motion
sensor after releasing a hanging mass of 0.05515 kg. For all three trials, the mass of weight 1 was
0.07545 kg, and the mass of weight 2 was 0.07535 kg. The first radius tested was 0.17 m in length, and
the inertia was found to be 0.004624 kgxm^2. Compared to the calculated theoretical inertia of
0.004358 kgxm^2, the percent error of this trial was 5.75%. The second trial tested a radius of 0.18m,
had an experimental inertia of 0.005255 kgxm^2, and a theoretical inertia calculated to be 0.004886
kgxm^2. The percent error of the second trial was found to be 7.02%. The third trial had a radius of 0.06
m, and the experimental and the theoretical inertias were found to be 0.001049kgxm^2 and 0.0005429
kgxm^2 respectively. The percent error was calculated to be 48.2%. Based on the theoretical and
experimental inertias collected, as the radius of the two weights decreased, the inertia decreased in
value as well. Possible sources of error in this experiment could have been due to the weights brushing
the rope of the pulley as they rotated.
The second experiment conducted tested how the shape and mass distribution of an object
affected rotational inertia. This was done by measuring the rotational inertia and the angular
acceleration of a spinning disk and a system of the spinning disk and the ring after a hanging mass of
0.02515kg was dropped for the disk system, and a mass of 0.5515 kg was dropped for the disk+ring
system. The rotational inertia of ring was found by subtracting the inertia found for the disk from the
inertia found for the disk and ring system. The angular acceleration for the disk was found to be 23.2
radians/s^2, and the Inertia of the disk was 0.000147 kgxm^2. For the ring+disk system, the angular
acceleration was discovered to be 11.2 radians/ s^2, and from that, the inertia of the ring+disk was
found to be 0.00674 kgxm^2. From these inertias, the inertia of the ring was found to be 0.00659
kgxm^2. Compared to the theoretical value of the inertia of the ring, which was calculated to be
0.0005074 kgxm^2, the percent error between the two were 92.3%. The percent difference between
the experimental and theoretical inertias of the disk+ring was also calculated to be 92.3%. Based on the
data collected for both the experimental and theoretical values, the disk had lesser inertia than the ring
had. From this information, it was assumed that this was due to the heavier weight of the ring and the
distribution of that weight around the circumference of the ring. Possible sources of error that could
have occurred in this experiment could be due to the string of the pulley getting wrapped around the
axel during experimentation.
Discussion:
1) A) Radius 1: I(Theory)=I(Theory for points)+I(Theory for rod)= 0.004358
kgxm^2+1/12M(rod)L^2=0.004358+1/12(0.0286)(2x0.17)=0.004634 kgxm^2
% Difference: (0.00462 mxkg^2-0.004634 mxkg^2)/0.004624 mxkg^2=0.00216 x 100= 0.216%
Radius 2: I(Theory)= I(Theory for points)+I(Theory for rod)=0.004886 kgxm^2+1/12M(rod)L^2=
0.004886 kgxm^2+1/2(0.0286)(2 x 0.18)= 0.005195 kgxm^2.
% Difference: (0.005255 kgxm^2-0.005195 kgxm^2)/0.005255 kgxm^2=0.0114 x 100= 1.14%
Radius 3: I(Theory)= I(Theory for points)+I(Theory for
rod)=0.0005429+1/12M(rod)L^2=0.0005429 kgxm^2+ 1/12(0.0286)(2 x 0.06)=0.0005772
kgxm^2
% Difference: (0.001049 kgxm^2-0.0005772 kgxm^2)/0.001049 kgxm^2=0.450 x 100= 45%
For every problem, the percent errors were improved upon, however trial two showed the most
improvement at a change of 5.88%. The second most improved trial was the first trial, and it
improved by 5.534%. The least improved trial was the third trial, and it had only improved by
3.2%.
B) The rotational inertia for the point masses was measured by subtracting the theoretical
inertia of the rod from the total experimental inertia in order to account for the extra rotational
inertia.
2)