May - 05-2015 Lab 16:Angular Acceleration

Lab 16

Purpose: Find a known torque to an object can rotate, and measure the angular acceleration and determine the moment of inertia by using the angular acceleration.

To achieve this, I will do this lab with two parts

Part 1:

Purpose of this part is to collect the basic data such as the weight of object, radius of pulley and disk, and angular acceleration of up and down and average.

Right side is the set up I do on this experiment.
1. Plug the power supply in to the Pasco rotational sensor; make sure that the computer is just reading the top disk.
2. Set up the computer. Open Logger Pro. Choose rotary motion and in option change the counts per rotation to 200
3. Make sure the hose clamp on the bottom is open so that the bottom disk will rotate independently.
4. Turn on the compressed air so that the disk can rotate separetely. Set the disks spinning freely to test the equipment.
5. Start the measurements and release the mass and get the angular velocity vs time graph and get angular acceleration up and down.






To do this correctly, I will do with six different experiments.
1 to 3 are changing the hanging mass from 25g to 75 g and keeping the disk and pulley same.
4 is keeping the 25g mass and disk  and changing the pulley to large one.
5 is keeping the 25 g mass large pulley and changing disk from steel to aluminum
6  is keeping the 25 g mass large pulley and changing disk to two steel disks.

I measure the equipment such as weight of mass and disk, and radius of pulley.

After finish this, I start to do the experiments.
First one:
is 25g mass, 1.36 kg steel disk, and 0.025 m diameter pulley

Second one:
is 50g mass, 1.36 kg steel disk, and 0.025 m diameter pulley

Third one:
is 75g mass, 1.36 kg steel disk, and 0.025 m diameter pulley

Fourth one:
is 25g mass, 1.36 kg steel disk, and 0.0495 m diameter pulley

Fifth one:
is 25g mass, 0.466 kg aluminum disk, and 0.0495 m diameter pulley

Last one
is 25g mass, 0.466 kg steel disk with 1.36 kg steel disk, and 0.0495 m diameter pulley

Here is all the data combine together:

As showing in picture, the angular acceleration up is bigger that angular acceleration down because there is friction on disk. When the mass is going down, the net torque is torque mass - torque friction , so angular acceleration down is smaller than the real. When the mass is going up, the net torque is - torque mass + - torque friction , so angular acceleration up is bigger than the real. Therefore, the real angular acceleration is the average.

Save those data to do next part to calculate the Moment of inertia. In part one, the error or uncertainty are easy to reduce because most of the mistakes are made by people who did this experiments such as the weight and radius. One thing should be reminded is that make sure to change to 200 counts per rotation and spin the disk independently.

Conclusion of Part one:

During part one, I measured the weight of disk and mass, radius of pulley, and angular acceleration for up and down; Seeing from my data, when increasing the hanging mass only, the angular acceleration is increasing as linear curve with a = m + C; when increase the radius of the pulley, the angular acceleration is increasing too as linear with a = r(pulley) + C; when increase the weight of disks, the angular acceleration is decreasing as linear with a = -M(disk) + C.

Part two:

Purpose of this part is to use the data from part one and calculate the moment of inertia by measurement and compare it with moment of inertia by formula and find the friction torque.

To find the moment of inertia

 I need to derive the function by drawing the force.









And using Newtons second and torque with force, angle and moment of inertia set up equation.

Here is the function I used to find Moment of inertia

Because I have done six different experiments



This is first one

Comparing the moment of inertia by using formula and by using measurement, the result I calculated is 3.8% off.

Second:

Comparing the moment of inertia by using formula and by using measurement, the result I calculated is 0.3% off.

Third:

Comparing the moment of inertia by using formula and by using measurement, the result I calculated is 0.339% off.

Fourth:

Comparing the moment of inertia by using formula and by using measurement, the result I calculated is 1.59% off.

Fifth:

Comparing the moment of inertia by using formula and by using measurement, the result I calculated is 0.35% off.

Last:


Comparing the moment of inertia by using formula and by using measurement, the result I calculated is 3.41% off.

Conclusion part two:

Second part of this lab is use the data in part one and derive the moment of inertia function. Plugging the data into the function, I obtained the experiment value (by formula) and original value (by measurement)of disk; the results are under 4% off.
The source of Uncertainty of this lab will be:
One, the data I measured such as weight and radius of disk and pulley have under 5 % off.
Two, when the disk spin, they may not all spin independently.
Three, the equipment may not function perfectly which may cause error two.