Tangental acceleration from given centripetal acceleration and a range of radii

[sneurlax]

Hi, how can I determine the tangental acceleration of a circle needed to produce a given centripetal acceleration from a range of radii? For example, I would like to produce 9.81 m/s/s centripetal acceleration with a range of radii from 5km to 100km? All I really need is to figure out the equation and I can write a program to graphically display the results.

Here's what I've found so far:

a_c = v_t²/r
centripetal acceleration = (tangental acceleration)² / radius of circular path

F_c = mv_t²/r
centripetal force = mass x ((tangental speed)² / radius of circular path)

If centripetal force is different than centripetal acceleration and a weight is needing to determine the Newtons involved then assume that the object being acted upon weighs 80 Earth kg.

Thanks for any help! If you could just nudge me in the right direction I'd appreciate it very much.

 

[Thaakisfox]

You don't need a tangential acceleration to produce a given centripetal acceleration, all you need is a given tangential speed. This can be calculated from the first formula you gave.

Vt^2=r*a_c
where r are the different radii and a_c is the centripetal acceleration.

 

[sneurlax]

... d'oh

That seems so obvious now.

Anyways, that means that an asteroid with a 137km circumference ring drilled into it (the longest manmade tunnel so far) would need to be accelerated to a spin 59.4km/h (instantaneous velocity tangental to the ring) to produce 9.81 m/s² acceleration... artificial gravity, anyone?