23- Sept.- 2014 Spinning Lab

Spinning Lab

Objective: 
1)Find the radius using centripetal acceleration and rotational speed

2) Find the relationship between omega (w) and angle (theta) for a particular apparatus.

Figure 1. the spinning apparatus with an
accelerometer taped on the edge and a
block of wood for reference to count rotations

Set up (2 of them):

1) Using a spinning apparatus and a accelerometer attached to it, you time how many times it makes 2 rotations. There are 5 trials at various accelerations. 

2) Using a specific apparatus with an electric motor, a stand, string and a rubber weight, we must time it in a similar fashion as set up 1 but for 5 rotations.

Part 1)

 Using the first set up, each class group made times of how long the wheel to turn 2 rotations and Prof. Wolf made an average period for each trial. We then graphed the results and made a linear fit to find the slope of omega vs. rotational acceleration (r) seen in (fig 2.):

Where a is acceleration and T is average period:

a= r*w^2

r= w^2

    a

since, w= 2(π)

               T

Then, r = a

                 T  

Figure 2. The resulting scatterplot with a linear fit of r= .1493 m

If we compare our theoretical radius r to the actual, we find that:

rtheo = 15cm

ract = 18 cm

17% more than theoretical

Part 2)

Figure 3. the rotating apparatus for this
lab.

 We now move on to the second set up in the lab. We use a spinning apparatus where the angle (theta) from the vertical effects the radius r (the faster it spins, the higher theta gets approaching 1.57 radians. The length of the string and the length in which the wood sticks out all affect r as well as the height h that the rubber end is from the ground. After putting all this in perspective, we derived the equation: where r= (Lstr + Larm)                     

w = [g*tan(theta) ] ^1/2      

[  (Ls + Larm)  ]       

After, we then recorded the trials and labeled our results on an excel spreadsheet. The biggest difference is between omega's both experimental and theoretical. We used our derived equation for omega experimental and for omega theoretical we used:

wtheo= 2(π)

         T

Figure 4. Our recorded data, very similar to most of our classmates' results since we all participated in each trial.

We then made a omega experimental vs. omega theoretical graph. Idealy their slope should come out to r = . The graph is not an ideal one but it is very close at a slope of r= .9926m . This comes out to less than a percent error for good results. What may have caused it was the stick flexing and friction in the system from air and the motor.

Figure 5. the resulting graph from our spreadsheet.
The ideal slope was supposed to be r=1

Figure 6. All recorded values for both part 1 and 2 an results for each trial and derivations of the equation for omega in part 2