# Optional Practical: Flying Pig

#### Introduction

In this practical the acceleration due to gravity will be found by measuring the time period of a pig flying in a circle. Note: this experiment can also be done with flying cows, dinosaurs and even planes. (With acknowledgement to Mark Headlee UWC USA)

#### Theory

The pig flies in a circle because there is a force acting perpendicular to its velocity (towards the centre of the circle). This force can be identified by drawing a free body diagram.

There is no vertical acceleration so Newton’s 1^{st} implies that the vertical component of forces are balanced so

F_{T}cosθ = mg

The pig is moving in a circle because there is an unbalanced force towards the centre, this force is provided by the horizontal component of tension

F_{T}sinθ = mω^{2}r

Dividing these equations gives:

F_{T}sinθ/F_{T}cosθ = ω^{2}r/g = tanθ

But tanθ= r/h

So r/h = ω^{2}r/g

And ω = 2π/T where T = time period

So 1/h = 4π^{2}/gT^{2}

h = gT^{2}/4π^{2}

#### Method

Devise a method to measure the time period and height h for at least 5 different lengths of string. Enter your values into a table not forgetting to estimate the uncertainties in both measurements.

From the equation it can be seen that T^{2} is proportional to h. Process your data so that you can plot a graph of T^{2} against h and use the gradient of the line to find a value for g.