13 May 2015. Inertia of Triangle.

Purpose

Part 1
to find the moment of inertia of a triangle being rotated at the center of mass (twice, with the width and the length on the bottom) experimentally.

Part 2
to find the moment of inertia of a triangle being rotated at the center of mass with calculation (true value) and compare it to the experimental value.

Apparatus:

Angular acceleration apparatus. This apparatus is built of pair of polished disks with a tiny hole that will accept air from the machine, to remove friction and allowing the disks to turn with minimal force. We will use a light hanging mass with a string tied around a torque pulley connected to the disks to provide torque, then measure the angular acceleration experimentally.

However, in this lab we used a disk that did not push air through it, plus now, we will attached triangle on top, as the picture shown.

Procedure and Data analysis

for this lab blog, the procedure and data analysis will be described individually under one part section. Since there are two parts of this experiment.


Part 1 (find the moment of inertia experimentally)

Procedure

1. Set up the apparatus so that it can measure the angle like our previous lab.
2. We need to measure the width, length, and weight of any apparatus used for data record.

3. We record the data of the angular acc. without any triangle mounted on it.
4. Then, with the triangle in the horizontal direction.
5. And the vertical direction.

Data Analysis

• First. recall that by measuring the angular acceleration of the system, we can determine the moment of inertia of the system.
• When the disk is spinning by itself. we will get the moment of inertia of this disk.
• Then, if the triangle is spinning, we will get the moment of inertia of the triangle plus the disk.
• So, the moment inertia of the triangle is the difference between moment of inertia of these measurements.
• Data recorded:

• And the radius of the large torque pulley is 0.025 m.

• We have, let's call it, three expt.: the disk by itself, the triangle in horizontal, and vertical.
• Now, we have data of angular position, angular velocity, and angular acceleration. The graph of angular acceleration vs time is useless due to the poor timing resolution of the sensors. So to get the angular acceleration we need to plot velocity vs time, and the slope is our answer! (Recall the kinematic equation ωt = ωo + αt)
• But,  we realize that there is some frictional torque happening here (even though we definitely minimize friction using air) as we plot the velocity vs time, one of the slope is higher when the mass is going down, meaning the acceleration is greater, and the acceleration is slower when the hanging mass is going up. (see the graphs)

Disk by itself

vertical triangle

horizontal triangle

• Therefore, for the angular acceleration, we need to find the average of these data.
• This the list of experiments that we did:

• So now, let's calculate it. Using the same concept from the last angular acc, lab, we can find the moment of inertia as follow.

• Now, let's simplify this equation as the mgr and mr^2 is always going to be the same, and calculate the moment of inertia.

Part 2 (find the "true" value of moment of inertia)

Data analysis

• First. we can find the moment of inertia of the triangle being rotated at the edge.

• Now, by the parallel axis theorem, we can find Icm.

• With L being the length of the triangle or the height of the triangle
• Now, we can calculate the moment of inertia of the triangle in vertical and horizontal direction.
• And the percent error.

Conclusions

• We manage to find the moment of inertia experimentally and the average percent error is approximately 5 %, so the result is pretty good.
• There are some small errors in this experiment that comes from;
• Some uncertainties when calculating the radius and others.
• Uncertainties from weighing the weight.