Julian's musings

Small angle approximations - an application


I thought a bit more about my previous post on small angle approximations, and decided it might be helpful to describe an application of the small angle approximations. While this example contains non-examinable aspects (at least in single maths A-level), the context should be fairly familiar (or can easily be demonstrated), and the mathematics is accessible to single maths students (at least as a demonstration). It also ties together ideas from mechanics and pure maths, so is helpful in this regard.

The question is: what is the period of a pendulum?

Small angle approximations


At a conference run by the BBO Maths Hub today, Jo Morgan mentioned that small angle approximations are a topic recently (re)introduced to the single maths A-level course, and many teachers may be unfamiliar with it.

During the day and on my journey home, I thought about this and some of the connections between it and other areas of the syllabus. So here are a few quick thoughts on ways we could think about them, making connections between this and other areas of the syllabus. I hope that this post offers some different perspectives on the topic.

Dividing fractions


Why is it that

\[\frac{3}{5}\div\frac{2}{3} = \frac{3}{5}\times\frac{3}{2},\]

or as the rule that students are frequently taught: “turn the second fraction upside-down and multiply”?

I’ve been inspired to revisit this question after listening to Ed Southall talking on Mr Barton’s Maths Podcast, where he mentioned this question.

In this post I suggest a teaching sequence which might lead to an understanding of the rule above, as well as a procedural knowledge of how to perform the rule.