# Torsional Pendulum Preliminary experiment

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Introduction

A2 Physics Coursework

Aim: To investigate a Torsional Pendulum.

Research and equations:

As we are working in circular motion, rather than linear motion, the equations that will help me investigate the Torsional pendulum will have to be derived. Here is how it is derived.

Using Force= Mass x Acceleration which is what you use for linear motion, this becomes Torque=Moment of Inertia x Angular acceleration. Using Force= -kx from a simple pendulum, this becomes Force=- Torsional Constant x Angular displacement

Therefore This can definitely be compared to a=-ω2x and becomes However therefore I then found out the exact expression which allowed me to directly work out I and K. The moment of inertia was simply mL2 However for the Torsional constant I first found the formula for the polar moment of inertia which was Ip=πd4/32 and the angle of twist φ=TL/GIp this was rearranged to T= GIp/L where T is the Torsional constant, then substituting in Ip I got Torsional constant= Using the equation I can now substitute in expressions for I and K to get an overall equation which came out to be: T=2π T=Time Period I=Moment of Inertia of the bar L=Length of wire G= Shear Modulus of material d= diameter of wire

The following web pages were used to help me derive these equations:

http://www.engin.umich.

Middle

To ensure that the experiment is carried out in safe environment I will make sure that I have plenty of space around me, with any obstacles removed to ensure the experiment can run smoothly.

Theory:

If simple harmonic motion applies, which I am

Conclusion

The value for the gradient I obtained was 0.4375, however I was expecting 0.5, therefore there is clearly errors in the time period and length, which is what determined the gradient, with reasons for these errors stated above. The error for the gradient will be the total error of the time and length, therefore approximately 6% error, when adding average most significant error of the time period and length.

Using the Equation T=2π I can work out the overall error of my experiment. As 2π x =T and as I found out that T=16.788 x l0.4375

Therefore 2π should be equal to 16.788 if my experiment had no errors. I will now work out how close to this value I actually got.

=2π = 14.12

Therefore the total error from what the true value should be is [(16.788-14.12)/16.788] x 100= 15.89%

From all the percentage errors above I can see that there are clearly issues with this preliminary experiment and that changes will have to be made for the final experiment to increase accuracy and reduce errors.

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