Lab #17 Finding the moment of inertia of a uniform triangle

Finding the moment of inertia of uniform triangle
Xuhong Zhao
Partners' Name: Amber Li and Daniel Negrete
05/13/2015

Purpose:
      Determine the moment of inertia of a right triangle thin plate around its center of mass, for two perpendicular orientations of the triangle.

Equipment:
      Disk, holder, triangle, hanging mass, string, sensor.

Measurement of the dimension and mass:

• The mass of the steel disk is 1357 grams
• The mass of the triangular plate is 456 grams
• The mass of the hanging mass is 25 grams
• The mass of the holder is 25 grams 
• The mass of the pulley is 36 grams
• The radius of the rotating pulley is 2.5 cm
• The high of the triangular plate is 14.8 cm
• The width of the triangular plate is 9.85 cm

Experiment:
    1. Set up the apparatus as the pictures show. Mount the triangle on a holder and disk. The upper disk floats on a cushion of air. A string is wrapped around a pulley on top of and attached to the disk. A string is wrapped  around the pulley and goes over a freely- rotating pulley to a hanging mass. The tension in the string exerts a torque on the pulley- disk combination.
    2. Turn on the air track and let the hanging mass, tie the hanging mass with the disk without the triangle.
    3. Let go the hanging mass, take the average angular acceleration of descending and ascending.
    4. Put the triangle horizontally on the holder, and repeat step three.
    5. Put the triangle vertically on the holder, and repeat step three.
    6. Based on the hanging mass and the angular acceleration, calculate the moment of inertia of each situation, and use the inertia with triangle subtract the one without triangle to get the inertia of triangle alone.
      7. Compare the theoretical value to actual value.

Conclusion:

  In vertical position. we find the difference between the experimental moment of inertia and theoretical moment of inertia is 0.000246-0.000239=0.000007,  that is about 2.8% error.

    In Horizontal position, we find the difference between the experimental moment of inertia and theoretical moment of inertia is 0.000555-0.000557=-0.000002, that is about 0.36 % error.

    There are some error could effect our experience. First of all, measurement exist error. We ignored the friction. I believe that our % error being less than 3% is very reasonable.