- #1

Cosmophile

- 111

- 2

I know that vectors have both magnitude and direction, while scalars only have magnitude. However, in solving problems and looking at how others have solved them, I've noticed something: vectors seem to be often written in "scalar form," if you will. For example, consider circular motion

[tex] \vec r = r(\cos \omega t \hat{\imath}+ \sin \omega t \hat{\jmath}) [/tex]

[tex] | \vec r| = r = constant [/tex]

[tex] \vec v = \frac {d \vec r}{dt} = r \omega (-\sin \omega t \hat{\imath} + \cos \omega t \hat{\jmath}) [/tex]

This all makes total sense to me. Where I find trouble, however, is that when I look around, I see people solve problems by simply saying ##v = r \omega##. No vector notation, no mention of direction, etc. How do they know to do this, and how can I know when to do this as well? This is causing me an unbelievable amount of frustration. Thanks!