Measuring g, but not knowing the centre of mass - problem?

[sexysam_short]

Hiya!

I'm confused, for my Physics A2 Coursework we're measuring g (gravitational field strength) and I don't know the centre of mass of the pendulum.

Will this affect my experiment and/or results? Should I do something to overcome it?

Please Help!

Sam(antha) xx

 

[krab]

Yes it will. You'll have to do a separate investigation to find the location of the centre of mass. Either that, or make an educated guess. Further, if the pendulum is a rigid mass that rotates about the pendulum pivot, it is actually a compound pendulum, and even the centre of mass won't tell you all you need. You'll need the moment of inertia. (But I can't imagine that the experiment is so poorly designed that you have to worry about these complications.)
You are best off if you can design your pendulum yourself. Then just make sure to make the length large compared with the size of the bob.

 

[sexysam_short]

Thanks loads! What are the advantages of the length being large compared with the size of the bob?

So, will it be ok if I just basically measure the length of the string that the pendulum is made from?

 

[krab]

Consider that the formula of the period is
$$T=2\pi\sqrt{l\over g}$$
If the bob is an extended mass of unknown composition 1 cm in size and the string is 1m long, the length to the c.of.m is 1.005m plus or minus 5mm. So the length $l$ can be thought of as uncertain by the bob size, 0.5% in the case of the example I just gave. This makes the period uncertain by .25%. If the bob was 10cm in size, the period uncertainty would be 2.5%.

 

[sexysam_short]

That makes loads of sense! Thank you lots again!