22-May-2017: Lab 17: PHYSICCS 4A LAB--Finding the moment of inertia of a uniform triangle.

Lab 17

Purpose:

To determine the moment of inertia of a right triangular thin plate around its center of mass, for two perpendicular orientations of the triangle.

Introduction:

In this lab, we will examine the parallel axis theorem with a special case. We will determine the moment of inertia of a right triangular at its edge. Then we will use parallel axis theorem to determine the moment of inertia around its center of mass. Comparing the result with the result of calculating the triangular part by evaluating the whole system’s moment of inertia. By comparing these two results, we can derive the conclusion that these two concepts are equal to each other in this lab.

Setup

Set the equipment up like the figure below. Mount the triangle on a holder and disk. The upper disk floats on a cushion of air.

Process:

Using LoggerPro to collect data when the apparatus is in the angular acceleration. Use the equation from Lab 16 as told in the guidance to derive the moment of inertia. First, determine the moment of inertia without triangle. The hanging mass we use in this step is 0.025 kg. The radius of the pulley is 0.0248 m. After determining these parameters, we begin the first part of experiment.

According the figure, we can get two angular accelerations. Using the equation from last lab, we can calculate the moment of inertia without triangle.

Then we put the triangle on the apparatus in an upright orientation. Then we determine the moment of inertia with triangle using the same method above. The data of this measurement is followed below.

With the equation from last lab, moment of inertia with triangle is

Then we change the edge of triangle to the longer edge like the figure below.

Then we perform the same steps above. From LoggerPro, we get this plot.

Here is the theory deriving of the second approach.

So in theory, the moment of inertia of a triangle is

Comparing these results, we get the conclusion that the result is quite close.

Conclusion:

In this lab, we tried to find two approaches for the moment of inertia of a triangle. The first approach is using the difference of the whole system’s moment of inertia and the apparatus’s moment of inertia. The second approach is finding a theory approach for this triangle. Some error occurs in this lab. The possible reason is the fitting error of the angular acceleration or the uncertainty of mass, radius and length of edge. From this lab, I learned about two ways to calculate a certain object’s moment of inertia. Overall, the lab is successful.