Circular Motion Due to Coriolis Force

[beth92]

Homework Statement

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.)

Homework Equations

Coriolis force, given by

F_C = -2m(ωxv)

The Attempt at a Solution

I started off by writing out the vector ω:

ω=ω_x+ω_y+ω_z

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:

F_C=-2m[(-ω_zv_y)i + (ω_zv_x)j + (-ω_yv_x)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!

 

[humanist rho]

Find net force on the particle in Earth's frame. (it may help.i'm not sure.)