Feynman Lectures on Physics - Rotation in 2 dimensions

[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.

Thanks for your help.

 

[tiny-tim]

Welcome to PF!

Hi ZirconiumAce! Welcome to PF!

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)

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! + …)

 

[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?

 

[ZirconiumAce]

I've got it.