# Does small angle mean small angular velocity?

• I
Why is the term ##(\sin\theta\,\dot{\theta})^2## fourth order in the small ##\theta##, as claimed by the sentence below (5.108)?

By small-angle approximation, ##(\sin\theta\,\dot{\theta})^2\approx\theta^2\,\dot{\theta}^2##.

For this to be fourth order, it seems like we must have ##\theta=\dot{\theta}##. Why is this true? What are the conditions for this to be true?

wrobel
For this to be fourth order, it seems like we must have θ=˙θ\theta=\dot{\theta}. Why is this true?
why quantities of different dimension must be equal? They must not. David Morin wrote a good book but definitely not for high school

why quantities of different dimension must be equal? They must not. David Morin wrote a good book but definitely not for high school

So is he right or wrong?

wrobel
So is he right or wrong?
My advice is that you should first think about your own understanding whether it is right or wrong.

My advice is that you should first think about your own understanding whether it is right or wrong.

My understanding is that ##(\sin\theta\,\dot{\theta})^2## is second order in ##\theta##. But that would mean that it cannot be ignored, since (5.109) contains second-order terms.

wrobel