May-8-2015 Lab 16: Angular Acceleration

Part 1 : We want to apply a known torque to an object that can rotate, and measure the angular acceleration. we can find a measured value for the moment of inertia. 





this is set up to do this lab. we can use it to measure the angular acceleration. 
































1.Before we start the experiment, we measured each of the following:


2. we plug the power supply into the Pasco ratational sensor. there is a cable with the yellow paint or tape, connect only that cable to the Lab Pro at Dig/Sonic 1, so the computer could read the top disk.

3. Set up the computer. Open Logger Pro. Choose Rotary Motion. there are 200 marks on our top disk, so we need to set the Equation in the Sensor Settings to counts per rotation. when we collect data, we can see graphs of angular position, angular velocity and angular acceleration vs. time. However, the graph of angular acceleration vs. time is useless due to the poor timing resolution if the sensors.

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. Set the disks spinning freely to test the equipment. 

6. With the string wrapped around the torque pulley and the hanging mass at its highest point, start the measurements and release the mass. 

EXPTS 1,2, and 3: we are going to look at the effect of changing the hanging mass(25 g, 50 g, 75 g). 

Here is graph of Expt 1: 



Here is graph of Expt 2 :

Here is graph of Expt 3: 

For Expt 1 and 4, we are going to look at the effect of changing the radius and which the hanging mass exerts a torque (small torque pulley, Large torque pulley). 

Here is graph of Expt 4: 

For Expt 4, 5, and 6, we are going to look at effect of changing the rotating mass(top steel, top aluminum, top steel + bottom steel).

Here is graph of Expt 5: 

Here is graph of Expt 6: 

After linear fit those angular velocity vs. time graphs, we can know the angular acceleration up and down for each Expt.

Then we calculated  the average of angular acceleration of each Expt, we write down all data we collected into a form:

From those graphs, the we could know the angular acceleration up is always bigger than the angular acceleration down because we cant ignore some frictional torque in the system. So, When the hanging mass is going down, the net torque is equal to torque mass - torque friction , so angular acceleration down is smaller than the real.

Conclusion: 
From this form, we could see For Expt 1,2, and 3, when the mass of hanging mass is increasing, the angular acceleration is increasing.
For Expt 1 and 4, with same hanging mass, when radius of torque pulley is increasing, the angular acceleration is increasing.
For Expt 4, 5, and 6, with same hanging mass, when the rotating mass is increasing, the angular acceleration is decreasing.


Part 2:

For this part, we can use our data (which from part 1) to determine the moment of inertia of each of disks.

Purpose:
we want to work out the torque of friction, Because there is some frictional torque in the system, the angular acceleration of system when mass is descending is not the same as when it is ascending.

First, let's call the counterclockwise direction of rotation positive and clockwise direction of rotation negative. Newton's second law would lead us to predict that:

Here is calculation for Expt 1: 

By formula, we calculated the inertia of disk is 0.0025556 kg*m^2



By measurement, we got the inertia of disk is 0.0026563 kg*m^2


Comparing the moment of inertia by using formula and by using measurement, the uncertainty is 3.8%. 





by formula, we can get the value of frictional torque = 0.000178 N*m 











Here is calculation for Expt 2: 

By formula, we calculated the inertia of disk is 0.0026553 kg*m^2



By measurement, we got the inertia of disk is 0.0026563 kg*m^2



Comparing the moment of inertia by using formula and by using measurement, the uncertainty is 0.3%.




by formula, we can get the value of frictional torque = 0.0002639 N*m 












Here is calculation for Expt 3: 

By formula, we calculated the
inertia of disk is 0.0026653 kg*m^2



By measurement, we got the inertia of disk is 0.0026563 kg*m^2



Comparing the moment of inertia by using formula and by using measurement, the uncertainty is 0.339%.




by formula, we can get the value of frictional torque = 0.000265 N*m 

Here is calculation for Expt 4: 

By formula, we calculated the
inertia of disk is 0.002614 kg*m^2



By measurement, we got the inertia of disk is 0.0026563 kg*m^2



Comparing the moment of inertia by using formula and by using measurement, the uncertainty is 1.59%.




by formula, we can get the value of frictional torque = 0.000341 N*m 

Here is calculation for Expt 5: 

By formula, we calculated the
inertia of disk is 0.0009133 kg*m^2



By measurement, we got the inertia of disk is 0.0009102 kg*m^2



Comparing the moment of inertia by using formula and by using measurement, the uncertainty is 0.35%.




by formula, we can get the value of frictional torque = 0.0003566 N*m 

Here is calculation for Expt 6: 

By formula, we calculated the
inertia of disk is 0.005152 kg*m^2



By measurement, we got the inertia of disk is 0.005313 kg*m^2



Comparing the moment of inertia by using formula and by using measurement, the uncertainty is 3.41%.




by formula, we can get the value of frictional torque = 0.0002868 N*m 

Conclusion :

For Expt 2, 3, and 5, their uncertainties that we calculated are very small(under 1%), we could say our predict values of inertia of disk is very close to the values of inertia of disk we measured.
However, for Expt 1, 4, and 6, their uncertainties are little bit big. our data, like radius and weight, we may made some mistakes for measuring them. and, during the disk spinning, top disk may not rotate independently with bottom disk.