8-May-2017:Angular Acceleration

In the past, we calculate the inertia of a disk, which is

but is there some other factors that we might mistakenly ignore. Today, we did a lab on different disks to see whether the real situation is matched what we calculate. 

Purpose

Calculate the disks' momentum of inertia to see whether it matches what we calculate.

Plan

We set the lab into two part. The first one is to collect data in different situations; the other one is using the data we collected to calculate the momentum of inertia.
First, we have to know some basic information about the disk like diameter and mass.
Then, set up the apparatus as follows.

Connect it with Logger Pro, then collect the data in different situations. 

Then, analyze the force on the system. 

On the disk and block, 

Then, we can know when it is going up

When it is going down

Solve these functions, we got 

Then, considering the friction force, we can get the functions from torque

After plugging everything, we can get 

Eventually, compare the data we get from the lab and calculation to see whether they are fit. 

Set up & Data

In the first experiment,
1. Measure each of the followings to significant figures
              Including the diameter and mass of the top steel disk, the bottom steel disk, the top aluminum disk, the smaller torque pulley, the larger torque pulley, and the mass of hanging mass.

2. Plug the power supply into the Pasco rotational sensor.

3. Set up the computer.
4. Make sure the hose clamp on the bottom is open so that the bottom disk will rotate independently of the top disk when the drop pin is in place.
5. Turn on the compressed air so that the disks can rotate separately.
6. With the string wrapped around the torque pulley and the hanging mass at its highest point, start the measurements and release the mass.
7. Change the hanging mass, torque pulley, and the top disk, collect data.
    Experiment 1, 2, and 3: effect of changing the hanging mass
    Experiment 1 and 4: effect of changing the radius and which the hanging mass exerts a torque
    Experiment 4, 5, and 6: effect of changing the rotation mass

In the second experiment,
1. by functions we calculate above, we can plug them into Excel to get inertia.
2. Calculate the inertia by the formula.

Analyze

From the table, we can know the percentage of difference are 

All of them are within 10%, which means the actual inertia is the same as calculating inertia if there is no other friction force and measure error. 

Conclusion

Through this lab, we could know the calculation of inertia is the same as the actual inertia. In general, we could know that the hanging mass or the magnitude of force does not effect the inertia, the change of radius and mass are exactly the same as we expected. The most error might be we do not know about the friction torque of disk, so we can only assume they are the same. Moreover, even though we use the air on the pulley, it still spun, which might take a part of the energy.