Angular Velocity in Curvilinear Translation?

1. Jun 24, 2012

c.teixeira

HI there.

Some days ago, whyle studying vector mechanics I came across with a rather dazzling doubt. Why isn't there angular velocity and accelaration in a curvilinear translation?

Imagine, a small planet in a perfect circular orbit around a star. Let's say, the planet has no form of rotation. Only translates around the star. It is rather dificult to admit that the planet has no angular and velocity and/or aceleration! Isn't angular velocity definied by the time rate of an angle? Isn't the planet angle varying with time?

Furthermore, every single particle in the planet is rotating around the star, right? If you consider just a particle, you can talk in angular velocity then, am I right?

Regards,

c.teixeira

2. Jun 24, 2012

cmmcnamara

Of course there is angular velocity and acceleration in curvilinear translation. However, unless the path selected closely resembles that of a circle (like your example), defining motion in terms of angular parameters does not present the easiest interpret able or usable information. In the case that the path followed is represented by some curve, it is much easier and intuitive to define motion using normal, tangential, and binormal directions as they are easier in general to evaluate along the path. For circular motion, angular definitions are more suitable because a circular path has a constant radius of curvature.

3. Jun 24, 2012