8-May, 15-May-2017: Lab 16: Angular acceleration

Purpose:

Learn the angular acceleration. Find out how the changing of hanging mass, rotating mass and the torque radius will influence on the angular acceleration.

Introduction:

In the angular acceleration lab, we usually use a disk. The changing of hanging mass, rotating mass and the torque radius affect on the angular acceleration. By changing one of those parameters and remaining others, we can find out how the chosen parameter will change the angular acceleration. For example, we can derive the influence of radius change by change the pulley’s size, which is made of the same material. After determining every parameters, we can finally find out how the changing of hanging mass, rotating mass and the torque radius will influence on the angular acceleration and verify it by the equation I*α=Torque where α stands for the angular acceleration.

Setup:

Set experiment devices as the following photo.

Procedure:

Measure the required parameters. Here are these parameters

	Top steel disk	Bottom steel disk	Top aluminum disk	Smaller torque pulley	Larger torque pulley	Hanging mass with apparatus
Mass(g)	1357	1348	466	9.99	36.59	24.62
Diameter(mm)	126.1	126.1	126.1	24.6	49.7

We use pasco rotational sensor to determine the rotation speed of the pulley. The data will be calculated and analyzed by Logger Pro. We will also use the compressed air to reduce friction and make the system smoother. Proceed several experiments with different conditions. And finally we can get data from Logger Pro.

Expt1:

Expt2:

Expt3:

Expt4:

Expt5:

Expt6:

By those data, we can derive the α from the sloop of the angular velocity. However, in the experiment we can see the angular velocity oscillated while it was changing. So we can get an approximate value with Logger Pro by matching it. Besides, there are two part of data. The first part is rising and the second part is falling. There are different sloops for them. We need calculate the average value of the α. The data are attached in the table below.

First, from expt 1, 2 and 3 we can derive the conclusion that when we increase hanging mass by x times, the average α will increase by x times, too. This can be verified from the equation I*α=Torque.From the data, we can derive several conclusions.

Second, from expt 1 and 4 we can derive that when we increase the radius of the torque pulley by x times, the average α will increase by x times, too. It satisfies the equation, too.

Third, from expt 4, 5 and 6 we can derive that when we change the material of the pulley with a x times density over the original density, the average α will increase by x times, too. It satisfies the equation, too.

In part2, we will use the data in part in to determine the moment of inertia of each of the disks with the following equation where m stands for the hanging mass and r stands for the radius of torque pulley.

With this equation and data from part1, we can derive the moment of inertia of each of the disks, which are all listed below.

Expt1	Expt2	Expt3	Expt4	Expt5	Expt6
0.024375	0.025731	0.025060	0.024465	0.008515	0.049461

For the expt1, 2 and 3, the moment of inertia is the same because they are made from the same material and have the same radius. However, from expt1 and 4 we can derive that when we only increase the radius of the pulley, the moment of inertia will stay the same. From exp4, 5 and 6, we can see that for different materials, the moment of inertia has an inverse relationship with the angular acceleration.

Conclusion:

In this lab, we learnt angular acceleration and found out that how the changing of hanging mass, rotating mass and the torque radius will influence on the angular acceleration. We also verify the influence with analysis to the equation I*α=Torque. Then we determine the moment of inertia of each of the disks with the given equation. We derived several conclusion from the relationship of different disks.