Ian1234
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#1
Report Thread starter 11 years ago
#1
Hi
I'm going through a physics past paper and in the mark scheme it says I need to use "a=(4(pi^2)r)/(T^2)" to substitute into another equation. I don't remember coming across this equation. What is it saying and do I need to derive it from another equaiton or just straight learn it?
Thanks
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Candescence
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Report 11 years ago
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Looks like its derived from keplers third law: t^2=(4r^3\pi^2)/GM

And then given g=GM/r^2 you get g=(4r\pi^2)/t^2

But you arent even expected to know keplers third law, you just need to be able to derive it from
 GMm/r^2 = mv^2/r
 GM/r=v^2
 v=2\pi r/T
 GM/r=4\pi^2r^2/T^2
 T^2=4r^3\pi^2/GM
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Ian1234
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Report Thread starter 11 years ago
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thanks for that
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Candescence
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Okay, that way is probably not what they're looking for, cause this would be so much easier:

a=v^2/r
 v^2 =(2\pi r/T)^2
 a=4\pi^2r^2/T^2r
 a=4\pi^2r/T^2

but the first way is more fun :P
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Ian1234
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Report Thread starter 11 years ago
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lol cheers. Thought the first method was a bit hard
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