22-May-2017: Lab 17: Finding the moment of inertia of a uniform triangle about its center of mass

Lab 17: Finding the moment of inertia of a uniform triangle about its center of mass

Author: Tian Cih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Date: May 22th, 2017

Purpose of the lab: measure Icm of a right triangle experimentally and compare with theoretical values (1/18 * M * B^2, done in video problems).

Theory: 1/18 * M * B^2 

By measuring angular accelerations (apply linear fit to velocity vs. time graphs) for both ways (up and down), we use the formula given in Lab 16 to determine the moment of inertia.
I = mgr / [(|alpha-up| + |alpha-down|) / 2] - mr^2 for both situations of naked apparatus and apparatus + triangle plate.

First we measure MoI for naked apparatus. Then we put a triangle onto this, and measure again. Then we reverse this triangle and do the same process.The subtraction of MoI combined and MoI "naked" is the MoI of the triangle plate. That is, Icm of a right triangle = I(apparatus + triangle) - I(apparatus)

Apparatus/Experimental setup: 

Holder and disk, triangle plate, hanging mass with string and "frictionless" pulley

Measured data:
Mass of triangle plate = 455 grams
Mass of hanging mass = 25 grams
Base of triangle plate = .098 meter
Height of triangle plate = .149 meter

Angular acceleration graphs for naked apparatus:

 Angular acceleration graphs for apparatus and vertically-placed plate combined:

 Angular acceleration graphs for apparatus and horizontally-placed plate combined:

Analysis:

Conclusions:

In this lab, we can see MoI don't match very well. The result is smaller than what we computed.The measurements of radius, lengths or heights contribute little to the inaccuracy. There are many possible reasons to cause this error.