23 September 2014: Spinning Lab 8

Objectives:
1) Finding the radius of a spinning object using centripetal acceleration and rotational speed
2) Finding the relationship between rotational speed, omega (w), and angle (theta) of a spinning system.

Part 1:
Materials:
1) Lazy Susan
2) Accelerometer
3) Timer
4) Logger Pro

Set Up:

An accelerometer was taped to the lazy susan.










Procedure:
Each group in the class was given a stopwatch. They were asked to time the time it took the lazy susan to turn 2 revolutions. These values were then reported and the professor took an average. This was repeated for 4 other trials in which the lazy susan was turned at varying speeds.

The professor then made a graph with all our values. The graph looked like this:

r=0.1493

From this graph we were able to determine from the slope that the radius=0.1493 m. This is possible because r= a/(w^2). (w^2) was calculated from the periods(T) we reported as w= (2pi)/T. And a was collected using the accelerometer.

So, finally:

r from data=0.1493 m

r in actuality= 0.18 m

So there is a 17% difference between both the radii.

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Part 2:

Materials:

1) Preset Setup

2) Timer

3) Ruler

4) Paper

Set Up:

It is important to note that we had nothing to do with this set up as it was done for us. This is a conical pendulum with a motor that allows for almost uniform rotation.

Procedure:

The first thing to do was to record the height of the system(h1), the length of the stick from which the pendulum hangs(d), and the length of the string from which the pendulum hangs(l).

h1= 210 cm

d= 62 cm

l= 177 cm

We then let the motor run and recorded data for 8 different trials. We were specifically recording at what height(h2) a rubber object tied to the end of the string hit a sheet of paper. This can be seen below:

The data that resulted can be seen below:

We were then required to derive an equation that would relate the angle between the stick and the string (theta) and angular velocity. Our equation can be seen below:

Using this data we plugged the following data into Logger Pro:

Lastly we created a graph of Omega vs F(theta). The graph looks like this:

Conclusions:

We took care in our derivation of our formula. We were also careful when plugging in numbers to create values. When creating our graph the graph is very close to 1 except for one dot. This shows that we have gathered good results.