The linear and rotational motions are independent, so after 2 min the bug has a z coordinate of .

Rotationally speaking, the bug starts on the y-axis at 10 cm ( ) and spins for 2 min. The angular speed is constant, so

==>

So in cylindrical coordinates the bug is at

after 2 minutes.

In rectangular coordinates we have

and

So

So

Using rectangular coordinates as the starting point, we have for spherical coordinates:

<-- Not the same as before!

So

Now, would normally be but since x is 0 this cannot be calculated directly. Suffice it to say that needs to be such that is positive and infinite. Thus . (The other way to see this is that in spherical coordinates is the same as in cylindrical coordinates.)

(As far as I know there is no exact expression of this.)

So in spherical coordinates we have:

-Dan