28- Oct. - 2014 Rotation Lab

Rotational Acceleration  Lab

Objective:

Figure 1. Lab apparatus for this set up.

  To see what factors affect angular acceleration α.

Set- Up:

 As seen in (fig 1.) we have a Pasco rotational sensor with a hanging mass, 2 steel disks and an aluminum one, two torque pulleys and a Lab Pro. We exchange different parts of this set up to change different variables to see what affects angular acceleration.

Data Collection:

Figure 2. The derivation of finding the inertia of the apparatus
as well as what affects angular acceleration. 

First we derived an equation for angular acceleration (α). We approached this problem as a dynamics problem with :

unequal net torque= (inertia of the system) *α

Since our torque will be known as well as the radius of the torque pulley (r), and inertia of our system the only unknown we would have is the average angular acceleration αavg.

We found this to be:

αavg = αup + αdown = MB*(g-asys.)r

                2                  Isys.

With this we find that if we get the sum of the absolute value of each (αup,  αdown) and average it, then we get the average angular acceleration. This is useful to compare resulting α's when we altar the main variables found in the other equation that can alter angular acceleration:

• Hanging Mass
• Radius of the torque pulley
• Inertia of the apparatus

With each of these in mind we performed 6 trials each changing one of these factors (seen in fig 2.). The first three trials were purely change in mass with a single steel disk as the system's inertia. The fourth trial altered only the radius of the torque pulley. The fifth altered both radius and system's inertia by using a lighter aluminum disk of same dimensions. The last altered the radius and doubled the inertia of a steel disk by having the hanging mass overcome 2 steel disks stacked and stuck together.

Figure 2. Our results for the 6 trials of our lab with recorded angular accelerations and αavg.

Conclusion:
From this we see that the apparent that the factors we found to affect angular acceleration all seem to have interesting relationships. When one looks at the results, doubling or even tripling the mass or radius has the same result as having half or a third of the inertia showing just like in our derived equation that they are inversely related. Any source of uncertainty comes down to the apparatuses air distribution and cleanliness of the disks as well as small imperfections of reading the rotations by the machine.