A lab problem--- moment of inertia

The calculation for the moment of inertia of the system.

Use the video capture to collect the disk from spinning to rest. Track a certain point as we marked at the edge of the disk. Build two calculations columns (Vx= x^2 and the other  Vy= y^2).

Then the tangential velocity is square root of  Vx+Vy

Tthe slope of the line is the tangential acceleration.
Once we find the a, the angular acceleration is a/r.
Assume we have a track and a 500-gram dynamics cart connected to the wheel. Calculate the time need for the cart travel from rest to 1 meter. the angle between the track and horizontal is measured as 46.6 degree.

the time required should be 7.55 second.

Do the experiment and conform the value. The time spent is 11.5 s.

It may have something wrong during the calculation.

I think the reason is the radius we used to convert the tangential acceleration to angular acceleration is 1/2 of the diameter. Should be smaller because the point marked on the wheel is not really on the edge of the wheel. Then the fractional torque is bigger, the time required for this traveling is longer.

 The second way of calculating the angular acceleration effect by the fractional torque.
Pick the points when the marked points at the top, and bottom.
As the times passed, collect a list of the points.

Type the data in excel.
B2==(B4-B3)/((A4-A2)/2)
C3=(B4-B3)/((A4-A2)/2)
then fill down. find the average of the C column which is the angular acceleration effect by the fractional torque.
repeat the same calculation as shown above. the time require is 11.87 s. Closed to our measurement.