Investigation into the affect of radius length on the speed and time period of one orbit

There are many things that will affect the out come in this experiment, the mass of the object in orbit, the length of the radius, gravity mulling it down to the centre of the earth, friction on the string in the rotation axis. I am going to look at how the radius affects the speed of one orbit.

I predict that as the radius increases the time taken for one orbit will also increase.

In fact if the radius doubles the time also taken for one orbit will also double. If we draw an arc of a circle with its centre of rotation at the apex of the angle ?, then the length of the arc (s, or 2s or 3s) is proportional to the length of the radius (r, or 2r, or 3r), so long as the arch always subtends the same angel ?.

On this information I am going to base my experiment on.

In this experiment I will need all these equipment:

Stopwatch

Bung

Fishing wire (as this will minimise friction as the bung rotates)

Ruler

10g weights

Method: Set up the apparatus in the diagram below. I will then measure the length of the radius starting at 10 cm and increase the length by 5cm each time. Using the weights I will keep it at a constant of 40g on the end nylon thread this will keep the tension in the wire. Using the sop watch we then timed the time taken for 10 complete orbits of the bung. We did this 4 times each and then took an average of all 4 sets of results to make a more reliable set of data. The data I have recorded is in the table below.

Radius

10

15

20

25

30

35

Exp1 a

6.66

7.19

8.88

9.65

11.19

12.24

Exp1 b

6.72

7.47

8.47

9.44

11.35

11.59

Exp2 a

6.53

7.04

9.50

9.44

11.22

11.75

Exp2 b

6.56

7.50

9.59

9.75

10.84

12.00

Average

6.61

7.30

9.11

9.57

11.15

11.89

I have plotted all of my on to graphs to make them understandable and easy to look at. From my graphs I can see that as the radius increases so does the time take for one orbit. But it does not double as the radius doubled. From a first look the graph suggests that the results increase by about 1.5. From my original prediction I would of expected to have results that follow my prediction. But this could have been due to the friction on the nylon thread and the affect of gravity on the bung. If well look at the diagram below we see that if the bung gets pulled down to the centre of the earth. The length of the radius is less than the measured radius.

But I have come to the conclusion that as the radius increases so does the time taken to orbit once. I think that my results were accurate to the equipment and the conditions in the lab. The results show a strong trend and this shows the results are accurate. In experiment’s 2a and 2b there are 2 anomalous results this is because the person that is spinning the bung could have speed up. The readings could only be take at the rate the speed the data travels to the eye and your brain tells you to click the stop on the stop watch.

This could be improved by using a laser stopwatch as this travels at the speed of light and is as fast as you can measure. If I were to look at this experiment and expand the research I could look at a number of other factors that will affect the experiment and change them. I could look at the affect of different weight on the end of the radius, or the amount of tension in the nylon thread.