Homework Help: Feynman Lectures on Physics - Rotation in 2 dimensions

1. Feb 12, 2012

ZirconiumAce

This isn't really a 'problem', I'm just trying to follow Feynman's reasoning in section 18-2 of Volume 1 The Feynman Lectures on Physics. I've attached a png of the paragraph in question.

I have 2 issues with this:

1. If the length OQ = OP, how can there be a right angle at P(x,y)?

2. I don't understand why QP = r $\Delta\theta$, rather than r * tan ($\Delta\theta$)

Am I missing something? I've checked the latest errata and this isn't mentioned.

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2. Feb 12, 2012

tiny-tim

Welcome to PF!

Hi ZirconiumAce! Welcome to PF!
Because that's the way these ∆s work …

we ignore anything that's small compared with a ∆ (in the same way that we ignore dh2, compared with dh, when we do calculus proofs)

So ∆θ = sin∆θ = tan∆θ.

(sin∆θ = ∆θ - (∆θ)3/3! + …)

3. Feb 12, 2012

ZirconiumAce

Ah yes a Taylor series. Mathematics back in the days of the slide rule I suppose. Now we don't bother with simplifications as much. Cheers! How about the right angle?

4. Feb 12, 2012

I've got it.