A particle has velocity v on a smooth horizontal plane. Show that the particle will move in a circle due to the rotation of the earth and find the radius of the circle. (Ignore all fictitious forces except the Coriolis force.)
Coriolis force, given by
FC = -2m(ωxv)
The Attempt at a Solution
I started off by writing out the vector ω:
But the x component of the earth's angular velocity is zero.
The velocity of the particle is horizontal, so has no z component.
So I tried calculating the cross product of ω and v and ended up with:
FC=-2m[(-ωzvy)i + (ωzvx)j + (-ωyvx)k]
This is where I got stuck..I'm not sure how I'm supposed to show that this causes circular motion. I'd assume I'm looking for a force perpendicular to v...
If anyone can give me any advice or let me know what I'm doing wrong I'd appreciate it!