How Is the Tangential Component of a Moving Particle Calculated?

[gorkin]

Homework Statement

Show that the tangential component of a moving particle is given by the expression a(tau)=v.a/v (upper a and v vectors) and the normal component is therefore
an = [a^2-(v.a)^2/v^2]^1/2. I have no idea how to solve this. Its from a book, not homework as such, just want to know how to solve it.

2. The attempt at a solution

 

[Astronuc]

an = [a^2-(v.a)^2/v^2]^1/2.

This part is simply an application of the Pythagorean theorem a² = a_t² + a_n², where a_t and a_n are perpendicular to each other.

see if this helps -

http://theory.uwinnipeg.ca/physics/circ/node5.html
http://theory.uwinnipeg.ca/physics/circ/node6.html