12-Nov.-14: Unknown Moment of Inertia

PURPOSE:

To determine the moment of inertia of a uniform triangle about its center of mass.

This will be accomplished by taking two measurements - one where we calculate the moment of inertia of the spinning apparatus without any attached masses, and a second calculation with the triangle attached. The difference in these two measurement should give us the moment of inertia of the triangle alone.


APPARATUS:









Equipment -

Near friction-less, air disk apparatus
Compressed air for the apparatus



EXPERIMENT:
The two parts to this activity included coming up with both a theoretical value and experimental (actual) value for the moment of the triangle.

1. Our first step was to measure the dimensions of the triangle, which we measured using digital calipers and a scale. Dimensions measured: 98.3-mm by 149.0-mm with a mass of 455-g.
2. We then calculated what the moment of inertia SHOULD be of a solid triangle with base B, height H and mass M, rotating about its center of mass.
   
   Calculation for horizontally secured triangle:
   
   
   
   Calculation for vertically secured triangle:
   
   
3. We then released the hanging mass on the apparatus so that it would begin its rotation. When the apparatus was in its rotation, we recorded the angular acceleration.
   
   Note: Because the hanging mass fights gravity on its way back up in the rotation, the angular acceleration is slightly different between when the mass descends and when the mass ascends.
   To account for this, we took the average of the two angular accelerations.
   
   
4. Using our new found equation for finding the moment of inertia of our apparatus, we found the difference between the moments with and without the triangle attached.
   
   

CONCLUSION:

Comparing the values we predicted to the values actually measured, we notice that they are off by a couple of decimal places.
I suspect that somewhere along the we took a wrong measurement OR perhaps the mass of the disk which the triangle was spinning on was supposed to be included in our calculations.

A Great Day for Physics

(11/17/14, 7:10am)