This part of the lab is to determine the moment of inertia of a mass  placed on the crossbar at several distances, , from the axis.

Remember the meaning of the various quantities during this experiment:

• is the “driving mass” hanging on the string
• is the moveable mass added to the crossbar; you are trying to find the moment of inertia due to this mass
• is the radius of the shaft; this value is to be used in your calculations of and .
• is the distance between mass and the axis of rotation. This parameter is not used in any calculation, but is an independent experimental variable.

PROCEDURE

1.   Mount a mass of unknown value,  and on each side of the crossbar (Figure 1) at a distance of your choosing, , from the shaft.

a.   Measure from the centre of the shaft to the centre of the masses and ensure that each mass is the same distance from the centre ().

b.   We will use total mass to indicate .

c.   The value of the mass, , will not be used in this part of the experiment, but will only be used when the experimental value of is compared with the theoretical value for the moment of inertia from Equation (3).  This comparison will be made in the graphical analysis portion of the lab (PART 4).

2.   To obtain the experimental value for , repeat steps 5 – 6 from PART 2 except now the attached masses of are set a distance away from the axis of rotation.

3.   Repeat this measurement 6 times for different values of and record your values in the table of the Results section for Part 3, as well as in Excel.

a.   Note: The mass is kept the same each time.

4.   The Excel sheet will then calculate the moment of inertia of your system, . Record these values in your table in the Results section.

5.   The Excel sheet will calculate the moment of inertia for the masses   by subtracting the measured value of by , i.e., .

Notice that you can find the value of by subtracting the measured value in this part of the experiment from the found in PART 2. At this stage, the value of that you obtain is the experimental value for the moment of inertia of mass (the two masses).  It is the experimental value because it is obtained from measured values of time and displacement, which effectively let you determine the rotational kinetic energy of the rotating system.