# Computing tangential and radial vector components of linear acceleration

I have to show that the tangential and radial vector components of linear acceleration are given by:

$$\bar a_{\rm{tan}}=\bar a \times \bar r \;\;\; \bar a_R=\bar w\times\bar v$$

I'm having a hard time with this one since it is using the cross-product and I have only just learned this concept. I'm not sure what vectors to cross.

Thanks for any help, and sorry I can't give you any of my work, but I can't find the information needed to be able to cross those vectors.

EDIT: Also, this is assuming this is a rigid object rotating about a fixed axis, in case that helps at all. I still don't know how to show this and I have looked at the text but can't find any examples or ideas on how to do this. Again, I appreciate any help.

## 1 Answer

Good question! I myself learnt it just now.

Pardon me for posting too many images. The following are extracts from 'Physics Part - 1 by Resnick and Halliday'. I personally feel that the material in this book is first rate!

This first image tells you how to determine the direction of the vector cross product. The second and third images answer your question about the cross product. Take time and read it patiently. Start reading from "Figure 11-11 shows the vectors.....  Here is a mathematical proof: 